Simpson S Rule Questions and Answers

Find the approximations T_n, M_n, and S_n for n = 6 and 12. Then compute the corresponding errors E_T, E_M, and E_S. (Round your answers to six decimal places.) int_1^4 4/sqrt(x) dx What observatio...

Use Simpson's rule with n = 4 to approximate the integral from 1 to 4 of (cos x)/x dx.

Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare your answer with the value of the integral produced by a calculator....

Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare your answer with the value of the integral produced by a calculator. y...

Approximate the area of the given curve using Simpson's Rule for n = 4 subintervals. The answer may be left as a sum in exact form without decimals. \int_{0}^{\pi} \sqrt{1 + \cos x}\ dx

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare the answer to the value of the integral produced by a calculator. (Round the answer to six decimal places.) y = xe^{-...

Consider the integral: \int_{0}^{\pi} \cos x\ dx a) Find the midpoint approximation M_4 b) Find the trapezoidal approximation T_4 c) Find the simpson's rule approximation S_8 d) Find the absolute...

Using the substitution method, evaluate the integral of (csc^2(1/x))(x^2) dx.

Use Simpson's rule with n = 10 subintervals to approximate the length of the curve. y = 3 cos x, (-pi/2, pi/2) Round your answer to four decimal places.

True or false? The error in Simpson's rule decreases by a factor of about 10,000 when n (even) is increased to 10n.

Evaluate the following integral using the Trapezoid Rule with n = 4 where a = 8. \int_{0}^{2} \sqrt{x^3 + a}\ dx Round your answer to 1 decimal place.

Suppose f(-1) = 2, \enspace f(0) = 3, \enspace f(1) = 4. Then using Simpson's rule to approximate \displaystyle \int_{-1}^1 f(x)\,dx, we obtain a. 6 b. 5 c. 4 d. 7

Let I = \int_1^4 \ln(x)\,dx. If you carry 4 decimal places in all calculations (rounded in the standard way), then the value of S_6 is closest to (A) 2.5447 (B) 2.3764 (C) 2.6981 (D) 2.4026 (E...

Use both the Trapezoidal Rule and Simpson's Rule to estimate the integral. Use n = 4 and use 4 decimals in your answers. \int_2^3 e^{\frac{3}{x}}\,dx

Find the value of \displaystyle \int_0^{0.6} e^x\,dx taking n = 6, correct to five significant figures, by using Simpson's one-third rule.

A radar gun was used to record the speed of a runner during the first 5 seconds of a race (see the table). Use Simpson's Rule to estimate the distance the runner covered during those 5 seconds. (Ro...

Evaluate \int_1^3 \sqrt{\ln 2x}\,dx using Simpson's Rule with n = 10.

Use Simpson's rule to numerically integrate the integral from 0 to 4 of x*ln(x + 1) dx; n = 6.

Given the following integral and value of n, approximate the following integral using the methods indicated (round your answers to six decimal places). \int_{0}^{1} e^{-3x^2} dx, n = 4 (a) Trapezoi...

Use Simpson's Rule to evaluate the integral int 2 to 4 (6x^2 - 7) dx. Choose n = 4.

The smallest number of subintervals needed to evaluate the integral int_0^1 (x-2)(x+3) dx exactly using Simpson's rule is(a) 1(b) 2(c) 4(d) We cannot find the exact value of the integral using Simp...

The graph of the concentration function c(t) is shown after a 7-mg injection of dye into a heart. Use Simpson's Rule to estimate the cardiac output.

The table gives the power consumption P in megawatts in a county from midnight to 6:00 AM on a day in December. Use Simpson's Rule to estimate the energy (in megawatt-hours) used during that time p...

Approximate the integral using the trapezoidal rule and Simpson's rule with the specified number of subintervals and then compare the answer with the exact value of the definite integral. Integral_...

Use Simpson's Rule to approximate the given integral for n = 4. integral_0^4 x^3 sin x dx

Use Simpson's Rule to evaluate the following integral by taking n = 4.

A river is 80 meters wide. The depth d in meters at a distance x meters from one end is given by the following table. (Table) Find approximately the area of cross-section of the river.

Use both trapezoidal and Simpson's Rule to evaluate \int_{-2}^{6} (x^{2} + 1)^{\frac{3}{2}} by taking n = 4.

Estimate integration from 1 to 5 sqrt(x)dx ; n = 8 by using Simpsons 1/3 rule of Numerical Integration.

Use Simpson's rule to approximate the given integral with the specified value of n. Integral_{1}^{5} 2 cos 3x/x dx, n=4

Using Simpson's Rule estimate the integral integral_0^4 (x^3 + x) dx with n = 4 steps and find an upper bound for |E_S|.

Estimate the definite integral using Simpson's Rule with n = 4. Round all calculations to three decimal places. integral 0^1 7 e^-x^2 dx

Approximate the area of the shaded region using the Trapezoidal Rule and Simpson's Rule with n = 4. (Round your answers to two decimal places.)

Given the following graph of the function y = f(x) and n = 6, answer the following questions about the area under the curve from x = 0 to x = 6. Use the Trapezoidal Rule to estimate the area, T6. U...

Use any one of L_{n}, R_{n}, M_{n}, T_{n}, or S_{n} to find a numerical approximation of \int_{0}^{3}\sqrt{1 + x^{3}} dx that is accurate to three decimal places and uses the smallest possible n. U...

Explain what is meant by the statement below: "When we use L_{n}, R_{n}, M_{n}, T_{n}, or S_{n} to approximate an integral we are really approximating the intergrand by a specific type of function...

Approximate the shaded area using n = 8. Round answers to the 6th decimal place and estimate the value using Simpson's rule with n = 8 rectangles.

Use (a) the Trapezoidal Rule and (b) Simpson's Rule to approximate the integral to four decimal places. Compare your results with the exact value. integral_0^pi 5 sin x dx; n = 4

An airplane's velocity is recorded at 5-minute (min) intervals during a 1-hour (h) period with the following results, in miles per hour: 505, 527, 549, 571, 59, 615, 637, 659, 681, 703, 725, 747, 7...

Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round the answer to four decimal places and compare the results with the exac...

Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round the answers to four decimal places and compare the results with the ex...

Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round the answers to four decimal places and compare the results with the exa...

Consider the function f x = e^fraction x^2 2. Find S8 on 0, 2. Round the answer correctly to five decimal places

Approximate the area of the shaded region using Simpson's Rule with n = 8.

Use the Simpson's Rule with n = 4 to approximate the definite integral integral 0^3 ln x dx.

Use Simpson's rule with n = 4 steps to estimate the integral. integral -1^1 x^2 + 4 dx

Calculate S_N given by Simpson's Rule for the value of N indicated. (Round your answer to five decimal places.) integral_0^3 dx/ x^3 + 3, N = 6

Consider the following integral: \int_{0}^{\pi} 27 \: sin(x) \: dx. Find the approximation S_{10}.

Use Simpson's Rule with n = 4 to approximate the integral \int_0^4 \dfrac{\sin x}{e^x}dx. Round your answer to 3 decimal places.

Use the Trapezoidal rule to approximate (to 6 decimal places) the integral integral_0^1 cos(x^2) dx with n = 4 and approximate the error using |E_T| less than or equal to (b - a)^3k_2 / 12 n^2.

Use the Trapezoid Rule and Simpson Rule with four subintervals to estimate integral 1^5 x^4 dx

Estimate the value of the integral \displaystyle{ \int\limits_2^5 xe^{ x/2} \mathrm{ d}x } using the Simpson s rule.

An airplane's velocity is recorded at 5-minute intervals during a 1-hour period with the following results (in miles per hour): 505, 527, 549, 571, 593, 615, 637, 659, 681, 703, 725, 747, 769. Use...

Calculate S_N given by Simpson's Rule for the value of N indicated. (Round your answer to five decimal places.) integral_0^3 dx / x^3 + 9, N = 6

Calculate T_N and M_N for the value of N indicated. (Round your answers to four decimal places.) integral_-1^1 4 e^x^2 dx, N = 5

Calculate S_N given by Simpson's Rule for the value of N indicated. (Round your answer to six decimal places.) integral_1^2 x^-2 x dx, N = 6

Water leaked from a tank at a rate of r(t) liters per hour, where the graph of r is as shown. Use Simpson's Rule to estimate the total amount of water that leaked out during the first 6 hours.

Show that \frac{1}{3}T_n+\frac{2}{3}M_n=S_{2n}.

The speedometer reading (\nu) on a car was observed at 1-minute intervals and recorded in the chart. Use Simpson's Rule to estimate the distance traveled by the car.

After a 6-mg injection of dye into a heart, the readings of dye concentration at two-second intervals are as shown in the table. Use Simpson's Rule to estimate the cardiac output.

A metal plate was found submerged vertically in seawater, which has density 64 Ib/ft^3. Measurements of the width of the plate were taken at the indicated depths. Use Simpson's Rule to estimate the...

Use Simpson's Rule with n = 6 to approximate \pi using the given equation. \pi = \int_{0}^{1/2} \frac{6}{\sqrt{1 - x^2}}dx

Use Simpson's Rule with n = 6 to approximate \pi using the given equation. \pi = \int_{0}^{1} \frac{4}{1 + x^2}dx

Prove that Simpson's Rule is exact when approximating the integral of a cubic polynomial function, and demonstrate the result for \ \displaystyle \int_0^1 x^3\ dx,\ n=2.

Use the Trapezoidal Rule and Simpson's Rule with n = 4, and use the integration capabilities of a graphing utility, to approximate the definite integral. Compare the results. integral_1^9 square ro...

Use Simpson's Rule with n = 6 to estimate the area under the curve y = (e^x)/x from x = 1 to x = 4.

Use Simpson's Rule with n = 10 to estimate the length of the sine curve y = sin x, 0 less than or equal to x less than or equal to pi.

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule with n = 10 to approximate the given integral. Round your answers to six decimal places. integral_1^4 square root x cos x...

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) integral_0^p...

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) integral_1^3...

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) integral_0^2...

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. integral_0^square root pi / 2 sin x^2 dx

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n=4. Compare these results with the approximation of the integral using a graphing utility. \int_{0}^{\pi/4}x\;\...

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n=4. Compare these results with the approximation of the integral using a graphing utility. \int_{3}^{3.1}\textr...

Use (a) the Midpoint Rule and (b) Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) Compare your results to the actual valu...

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) \int_{0}^{1}...

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) \int_{0}^{4}...

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) \int_{1}^{3}...

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) \int_{2}^{3}...

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule. Compare these results with the approximation of the integral using a graphing utility. \int_{1}^{7}\frac{\sqrt{x-1}}...

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule. Compare these results with the approximation of the integral using a graphing utility. \int_{3}^{6}\frac{1}{1-\sqrt{...

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule. Compare these results with the approximation of the integral using a graphing utility. \int_{-2}^{2}\frac{1}{x^2+1}\...

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule. Compare these results with the approximation of the integral using a graphing utility. \int_{0}^{1}\frac{1}{x^2+1}\;...

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule. Compare these results with the approximation of the integral using a graphing utility. \int_{0}^{1}\sqrt{x}\sqrt{1-x...

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule. Compare these results with the approximation of the integral using a graphing utility. \int_{0}^{2}\frac{1}{\sqrt{1+...

Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exa...

Use the Trapezoidal Rule and Simpson's Rule with n = 4, and use the integration capabilities of a graphing utility, to approximate the definite integral. integral_0^1 ({x^2} / 2 + 1) dx

Approximate the definite integral using (a) the Trapezoidal Rule and (b) Simpson's Rule. \int_{0}^{\pi} \sqrt{x}\;\textrm{sin}\;x\;dx, \; n=4

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) \int_{0}^{4}...

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) \int_{0}^{2}...

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. y = ln (1 + x^3), 0 less than or equal to x less than or equal to 5

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. y = cube root of x, 1 less than or equal to x less than or equal to 6

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. y = e^{-x^2}, 0 less than or equal to x less than or equal to 2

Evaluate the integral int_2^4 sqrt x dx using the Simpson's rule and n = 4.

Use the error formulas for the Trapezoid rule and Simpson's rule to find the maximum error in the approximation of the definite integral integral_1^4 x^{6 / 5} dx with n = 4. Round your answers to...

Use 4 sub-intervals to approximate integral_{0}^{{2 pi} / 3} cos (x) dx and calculate as good a bound as possible on the error using Simpson's Rule. Give your answer as a decimal accurate to at lea...

Use the Simpson's Rule to approximate the following integral with the specified value of ''n'': \int_{0}^{4} e^{4 \sqrt{t}} sin(4t) \: dt, \; n =8.

Approximate the following integral using Simpson's Rule: \int_{0}^{3x/5} 5 \: sin(10x) \: cos(5x) \: dx = \dfrac{4}{3}. Experiment with values of ''n'' to ensure that the error is less than \rm 10^...

Approximate the following integral using Simpson's Rule. Experiment with values of n to ensure that the error is less than 10^{-3}. integral_0^{pi / 3} 3 sin (18 x) cos (9 x) dx = 4 / 9

Evaluate the following integral using the Simpson's rule with 6 equally segments: \int_{0}^{6} \sqrt{4+x^2} \: dx.

Use the Simpson's rule with n=6 to approximate the area under the right half of the Gaussian distribution function corresponding to mean 0 and standard deviation 1, i.e., approximate integral from...

How large must n be to guarantee that the Simpson's rule approximation for integral from t=0 to pi/2 of sin(3t+1) dt is accurate to within 10^(-5)?

Use the Simpson's Rule to approximate the following interval using n = 6: \int_{0}^{3} \dfrac{1}{8 + y^5} dy.

Use the trapezoidal rule, the Midpoint, and Simpson's rule to approximate the given integral with the specified value of n. \int_1^4 6\sqrt{\ln{x}}dx,\; n = 6

How large do we have to choose n so that the approximation in Simpson's rule to the integral from 0 to 1 of (e^x + 4x^5)dx is accurate up to 0.00001?

Integrate the integral 3 1 ln ( ln ( 2 z ) ) d z , numerically using Simpson's rule and six intervals.

Use the Simpson's Rule, to find the given integral with the specified value of n. int_{1}^{4} 9 square root{ln x} dx, n=6

Use the Simpson's Rule, to find the given integral with the specified value of n. int_{1}^{5} 2 cos (2x)/x dx, n=8.

Find the integral of e^{-x} dx from x = 0 to 1 with Simpson's rule using 10 strips.

A function f is given by the following table: Approximate the area between the x-axis and y = f (x) from x = 0 to x = 4 using Simpson's Rule.

Use 4 sub-intervals to approximate 7 2 0 e x d x and calculate as good a bound as possible on the error using Simpson's Rule. Give your answer as a decimal accurate to at least 6 decimal plac...

(a) Find the exact value of \int_2^6\frac{dx}{\sqrt{x}}. (b) Using 4 intervals (by hand), find an approximate value of \int_2^6\frac{dx}{\sqrt{x}}. (c) Find the error bound specified by Simpson's R...

Evaluate the integral. \int_{-1}^{1} \frac{2+xe^{|x|}}{1+x^2}dx

Use the Simpson's Rule to approximate the given integral with the specified value of ''n'': \int_{1}^{5} \dfrac{6 \: cos(4x)}{x} dx, \; n = 8.

Use the Error Bound to find the least possible value of N for which E r r o r ( S N ) (= 1 10 9 in approximating 1 0 3 e x 2 d x using the result that E r r o r ( S N ) (= K 4 ( b a...

\int_{-1}^{1} \frac{1}{\sin x + 7} dx a) Approximate the definite integral with the Trapezoid Rule and n = 6. b) Approximate the definite integral with Simpson's Rule and n = 6.

Let f(x) = e^{x^2}. It can be shown by direct computation that f^{(4)}(x) \leq 76e on the interval \left [ 0,\; 1 \right ]. Using this information and the appropriate error formula, how large shoul...

Approximate to five decimal places the area under the curve y=sin x over the interval [0, pi] using Simpson's Rule with n=4.

How large should n be to guarantee that the Simpson's Rule approximation to \int_{0}^{1} 17e^{x^2} is accurate to within 0.0001? n \geq _____

Approximate the definite integral \int_{3}^{7} |4-x| dx using 4 subintervals of equal length and (a) midpoint rule, (b) trapezoidal rule, (c) Simpson's rule.

How large should n be to guarantee that the Simpsons Rule approximation to \int_1^3 (-x^4 + 8x^3 - 18x^2 + 2x + 3)dx is accurate to within 0.01?

Use the Simpson's rule to approximate the given integral with the specified value of n. int_{0}^{4} 5 cot (square root{2x}) dx, n=10

Use Simpson's to approximate the given integral with the specified value of n. int_{1}^{5} 2 cos(2x)/x dx, n=8.

Use Simpson's rule to approximate the given integral with the specified value of n. int_{1}^{4} ninth root of{ln (x) } dx, n=6.

Use Simpson's Rule to evaluate the following integral. Let n = 8. Round to 4 decimal places. integral_0^(2pi) cos^2 (x) dx

Estimate the error if S_8 is used to calculate \int_0^5 \cos(3x)dx.

Use the Simpson's Rule to approximate the given integral using 4 equal subintervals: \int_{1}^{2} \dfrac{ln(x)}{5+x} dx.

Use the Simpson's Rule to approximate the given interval with the specified value of ''n'': \int_{2}^{3} \dfrac{1}{ln(t)} \: dt, \; n = 10.

Use the Simpson's Rule to approximate the given interval with the specified value of ''n'': \int_{0}^{4} \sqrt{y} \: cos(y) \: dy, \; n = 8.

Use the Simpson's Rule to approximate the given interval with the specified value of ''n'': \int_{1}^{3} e^{1/x} \: dx, \; n = 8.

Use the Simpson's Rule to approximate the given interval with the specified value of ''n'': \int_{0}^{4} x^3sin(x) \: dx, \; n = 8.

Use the Simpson's Rule to approximate the given interval with the specified value of ''n'': \int_{0}^{\pi/2} \sqrt 3 {1+cos(x)} \: dx, \; n = 4.

Use the Simpson's Rule to approximate the given interval with the specified value of ''n'': \int_{0}^{2} \dfrac{1}{1+x^6} \: dx, \; n = 8.

Use the Simpson's Rule to approximate the given interval with the specified value of ''n'': \int_{0}^{2} \dfrac{e^x}{1+x^2} \: dx, \; n = 10.

Use the Simpson's Rule to approximate the given interval with the specified value of ''n'': \int_{1}^{2} \sqrt{x^3 -1} \: dx, \; n = 10.

Use the Simpson's rule with n = 4 to evaluate: \int_0^{2} \sqrt{1 + x^3}dx.

Give the following definite integral and n=4. int_{0}^{1.5} sin (x^2) dx. Use Simpson's rule to approximate the definite integral.

Approximate the value of the definite integral using the Trapezoidal Rule and Simpson's Rule for the indicated value of n. Round your answers to three decimal places. \int_{0}^{3} \frac{x}{8 + x +...

Estimate the minimum number of subintervals to approximate the value of \displaystyle \int_{-2}^5 9\:sin(x+5)dx with an error of magnitude less than 2 \times 10^{-4} using the error estimate formul...

How large should n be to guarantee that the Simpson's Rule approximation to the integral from 0 to 1 of 9e^(x^2) dx is accurate to within 0.0001?

Use both the trapezoid rule and Simpson's rule with n = 6 to approximate the arc length of the curve y = e^(x^2) for x from 0 to 1. (Round your answers to three decimal places.)

Give an integral that gives the length of the curve y = \tan x from x = 0 to x = \dfrac{\pi}{4}. Use Simpson's rule with 20 subintervals to approximate the value of this integral.

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule. Compare these results with the approximation of the integral using a graphing utility. (Round your answers to four d...

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule. Compare these results with the approximation of the integral using a graphing utility. Round your answer to four dec...

By using Simpson's rule and dividing the interval [0,3] into 6 equal subintervals approximate the integral int_{0}^{3} Square root{1+x} dx.

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. \\ y = x\sin x,\ 0 \leq x \leq 2\pi

Find the integration of 3 1 s i n x d x Using: 1. Trapezoidal (4). 2. Simpson's Rule (8).

Use Simpson's rule with n=4 to estimate the area under the curve of y=ln x from x=2 to x=6. How many places accurate is this compared to the actual area under the curve?

Evaluate the integral of the given tabular data with Simpson's 1/3 Rule. x -2 0 2 4 6 8 10 f(x) 35 5 -10 2 5 3 20

Find the integration of integral from 1 to 3 of sin(x) dx using: A) Trapezoidal. B) Simpson's Rule.

The following table gives the power consumption in megawatts for a region from midnight to 6:00 AM on a particular day. [TABLE] Use Simpson's Rule to estimate the energy used during this time perio...

Integrate integral_4^{12} x exp (-{(x - 4)^2} / {3}) dx.

Estimate the area under a curve using Simpson's method.

Evaluate the integral. integral_{-10}^{10} {e^{{10} / x} / {e^{{10}/x} +1} dx

Use the error formulas to find the smallest n such that when \int_{0}^{20}sin(3x)dx is approximated using the trapezoidal rule and Simpson's rule, the error is less than 10^{-4}.

Use the trapezoid rule and Simpson's rule to approximate the value of \int_{0}^{8} x \sqrt{x^2 + 7} \; \mathrm{d}x with n = 4. Then find the exact value of the integral.

Surveying suggests that, while the water-silt boundary may still be regarded as having cylindrical symmetry about the axis of the original borehole, a more accurate profile can be obtained from the...

Use Simpson's Rule with n = 6 to estimate the length of the arc of the curve with equations x = t^2, y = t^3, z = t^4, 0 less than or equal to t less than or equal to 3.

Solve by using Simpson's rule: \int_0^2 \sqrt{x^3 + 1} dx, n= 4

Solve by using Simpson's rule: \int_2^4 \frac{1}{x^2 + 1} dx, n = 10

Use Simpson's rule: \int_{0}^{2}\sqrt{x^{3}+1} dx, n=4

Use Simpson's rule: \int_{2}^{4}\frac{1}{x^{2}+1}dx, n=10

A study was done on the mortality (live vs. die) of two major hospitals: CareBetter and TreatMore. Data were collected over a period of time from five major illnesses and it was found that CareBett...

Use Simpson's Rule to approximate the average value of the temperature function f(x) = 37\sin (2\pi /365(x - 101)) + 25 for a 365-day year. This is one way to estimate the annual mean air temperatu...

Use Simpson's Rule with n = 10 to approximate the length of the arc of r(t) = ti + t^2j + t^3k from the origin to the point (2, 4, 8).

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Compare your result with the exact value of the integral. (Give your answers correct to 4 decimal plac...

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. (Give your answers correct to 4 decimal places.) \int_{0}^{3}4(1+x^{3})^{1/2};n=4

Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare your answer with the value of the integral produced by a calculator. (...

How large should n be to guarantee that the Simpson's Rule approximation to the integral int_0^1 13e^{x^2} is accurate to within 0.00001?

Given the following definite integral and n = 4 . Answer the following questions. 1.5 0 sin ( x 2 ) d x 1. Use the Trapezoidal Rule to approximate the definite integral. 2. Use the Midpoint Rul...

Using Simpson's Rule: Estimate the integral int_0^pi (4sin(x)dx with n = 4 steps and find an upper bound |E_S|. |E_S| less than or equal to _____ Now evaluate the integral directly and calculate...

Use the calculator and Simpson's rule to integrate: \int_{0}^{3}2x^3dx , n = 6

Use Simpson's Rule with n = 4 to estimate the arc length of the curve, L. Give your answer to six decimal places. y = sec (x), 0 less than or equal to x less than or equal to pi / 3

Estimate the area under the curve in the interval [0, 3] with n = 6 using Simpson s Rule.

Which formula, Trapezoidal or Simpson s, gives the better approximation when using the same number of terms in the expansion? Why?

Use Simpson's Rule with n = 4 to estimate the arc length of the curve, L. Give the answer to six decimal places. y = sec(x), 0 less than or equal to x less than or equal to pi / 6.

Use the following table to estimate the value of the integral from 4 to 19 f(x)dx using Simpson s rule.

Given the table below. Approximate the total volume of water that passed through the dam from t = 1 to t = 13, with n = 6 using Simpson s rule.

Using the integral from 0 to 1 1/x+1 dx, n = 6, How many subintervals would be needed for Simpson's approximation for the error to be less than 0.00001?

Using the integral from 0 to 1 1/x+1 dx, n = 6, Approximate the integral using Simpson's rule.

Use Simpson's Rule to approximate the given integral with the specified value of n. int_0^4 ln(6 + e^x)dx, n = 8

The following table gives the approximate amount of emissions E of nitrogen oxides in millions of metric tons per year in the US. Let t be the number of years since 1940 and E = f(t). Estimate the...

Given int 0 4 sqrt(x) dx. Approximate the definite integral with the Simpson's Rule and n = 4.

Use Simpson's Rule with n = 10 to approximate 2 1 1 x d x

Use Simpson's Rule with n = 10 to approximate \int_1^2 \dfrac{1}{x}\ dx.

Approximate the definite integral using the Trapezoidal Rule and Sympson's Rule. Compare these results with the approximation of the integral using a graphing utility. (Round the answers to four de...

Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exa...

Approximate the definite integral using the Trapezoidal rule and Simpson's rule with n=4. (Round your answers to three decimal places.) Integral_{0}^{5} 5xe^{-x} dx

Use the Trapezoidal and Simpson's rules to calculate the following definite integral. I = \int\limits_1^6 {{2 \over {{{\left( {3x - 2} \right)}^{{3 \over 4}}}}}} dx

Use the Trapezoidal and Simpson's rules to calculate the following definite integral. I = 3600 \cdot \int\limits_0^{12} {\left( {12{t^2} - {t^3}} \right)} dt

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. \int_0^2 {5x{e^{ -...

Estimate integral_0^{16} x^2 dx using SIMP(2).

Use Simpson's rule with n = 6 to approximate: integral_1^4 1 / x^2 dx. Give the answer correct to 4 decimal places.

Find n such that the error in approximating the given definite integral \int\limits_0^5 x^4 \text{d}x is less than 0.0001 when using: a) the Trapezoidal Rule, b) the Simpson s...

Find n such that the error in approximating the given definite integral \int\limits_1^4 \frac{1}{\sqrt{x}} \text{d}x is less than 0.0001 when using: a) the Trapezoidal Rule, b)...

Find n such that the error in approximating the given definite integral \int\limits_0^\pi \sin x \text{d} x is less than 0.0001 when using: a) the Trapezoidal Rule, b) the Si...

Use Simpson's rule to calculate the following definite integrals: displaystyle I_1 = 3600 cdot int^{12}_0(12t^2 - t^3)cdot dt and displaystyle I_2 = int^6_1 dfrac{2}{(3x - 2)^{3/4}} cdot dx

Use Simpson's rule with n = 4 to approximate the integral from 1 to 4 of 1/x^2 dx.

Estimate the minimum number of subintervals to approximate the value of \int_0^9 \sqrt{7x+6}dx with an error of magnitude less than 5 \times 10^{-4} using a. the error estimate formula for the Tra...

a. Approximate the area under the curve f(x) = 1/square root x and above the x-axis by splitting the region from x = 1 to x = 9 into 8 equal subintervals (rectangles) and using the left endpoints o...

Use the error formula to find n such that the error in the approximation of the definite integral is less than or equal to 0.0002 using Simpson's Rule. integral_0^{pi/4} cos (x^2)dx

How large should n be to guarantee that the Simpsons Rule approximation to Integral_{-2}^{2} (-x^4 + 0x^3 + 24x^2 + 4x -3) dx in accurate to within 0.01.

Estimate Integral_{0}^{1} e^{-x^2/2} dx using Simpson's Rule with n=10. Report your estimate to 6 decimal places.

Use Simpson's rule to approximate integral_0^4 x^3 dx with n = 8.

In approximate the definite integral with the Trapezoidal Rule and Simpson's Rule, with n=6. Integral_{1}^{-1} 1/sin x+2 dx

In approximate the definite integral with the Trapezoidal Rule and Simpson's Rule, with n=6. Integral_{1}^{4} In x dx

In approximate the definite integral with the Trapezoidal Rule and Simpson's Rule, with n=6. Integral_{0}^{pi/2} square root{cos x} dx

In approximate the definite integral with the Trapezoidal Rule and Simpson's Rule, with n=6. Integra_{0}^{x} x sin x dx

In approximate the definite integral with the Trapezoidal Rule and Simpson's Rule, with n=6. Integral_{0}^{2} square root {x^2+1} dx

In approximate the definite integral with the Trapezoidal Rule and Simpson's Rule, with n=6. Integral_{-3}^{1} e^{x^2} dx

In approximate the definite integral with the Trapezoidal Rule and Simpson's Rule, with n=6. Integral_{0}^{1} cos(x^2) dx

Use Simpson's Rule to approximate the integral. Show values of h, yo, y1, etc. \int_2^4 dx/(x^2 + 1); n=8

Approximate the following definite integral, with the Trapezoidal Rule and Simpson's Rule with n = 6 1 0 x 2 + 1 d x

Approximate the following definite integral, with the Trapezoidal Rule and Simpson's Rule with n = 6 1 0 cos ( x 2 ) d x

For the following definite integral, (a) Approximate the definite integral with the Trapezoidal Rule and n = 4 (b) Approximate the definite integral with Simpson's Rule and n = 4 . (c) Find the...

int_{1}^{4} frac{1}{sqrt{x}}dx Find n such that the error in approximating the given definite integral is less than 0.0001 when using: (a) the Trapezoidal Rule (b) Simpson's Rule

Use Simpson's Rule to approximate \int_{1.0}^{2.8} f(x) dx using the following data points. |x |1.0 |1.3 |1.6 |1.9 |2.2 |2.5 |2.8 |f(x) |3.2 |4.1 |5.2 |4.6 |4.2 |5.1 |5.7

(a) Evaluate int 1 2 dx / x2 by using Simpson's Rule with n = 4. (b) Find a bound on the error in approximating the definite integral using Simpson's Rule.

Evaluate the integral: 0 sin 6 x cos 4 x d x .

(a) Evaluate \int^2_1 \frac {dx}{x^2} by using Simpson's Rule with n = 4. (b) Find a bound on the error in approximating the definite integral using Simpson's Rule.

A definite integral is given: Integral from 0 to 4 of sqrt(x) dx. A) Approximate the definite integral with the Trapezoidal Rule and n = 4. B) Approximate the definite integral with Simpson's Rule...

Approximate the following integrals using Simpson's rule using the given value of n: \int_2^6 \dfrac{dx}{x + 3},\ \ n = 10

Approximate the following integrals using Simpson's rule using the given value of n: \int_0^4 2^x\ dx,\ \ n = 12

Approximate \int_0^3 \dfrac{dx}{1 + x} using Simpson's rule, where n = 6 to 4 decimal places.

Use the Error Bound to find the least possible value of N for which Error(S_N) \leq 1 x 10^{-9} in approximating \int_0^1 6e^{x^2} dx using the result that Error(S_N) \leq \dfrac{K_4 (b - a)^5}{1...

Suppose that the accompanying table shows the velocity of a car every second for 8 seconds. Use Simpson's Rule to approximate the distance traveled by the car in the 8 seconds. Round your answer to...

Use the Trapezoidal Rule and Simpson's Rule to approximate the results with the exact value of the definite integral. \int_{1}^{2} \left ( \frac{x^2}{4} + 6 \right ) dx, n = 4 Exact: Trapezoidal: S...

Find the vectors T, N, and B at the given point. r(t) = (3cos t, 3sin t, 3ln cos t); (3, 0, 0)

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) \int_0^1\sqrt{3z}e^{-4z...

Given the following integral \int^1_0 \frac {16 (x - 1)}{x^4 - 2x^3 + 4x - 4}dx a. Evaluate the above integral. b. Let the step side to be 0.1, apply the Simpson's rule to obtain a numerical sol...

Estimate using Simpson's rule with n = 6 subintervals for \int_{-3}^{4} f(x) dx.

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. (Round your answer...

Use Simpson's Rule and the Trapezoid Rule to estimate the value of the integral \int_{-3}^3(2x^3 - 2x^2 - x - 3)dx In both cases, use n = 2 subdivisions Simpson's Rule approximation S_2 = [{Blan...

Approximate the following integral using the methods indicated with n = 4 subdivision. integral from 0 to 1 of e^{-2x^2} dx

Suppose you are asked to estimate the volume of a football. You measure and find that a football is 28 cm long. You use a piece of string and measure the circumference at its widest point to be 53c...

What is Simpson's rule and how to use it? Give some examples.

Use Simpson's Rule with n = 4 to estimate the arc length of the curve y = 1 e^{-2 x}, 0 less than or equal to x less than or equal to 2.

Estimate the area under the curve f(x)=?x+1 in the interval [0, 4] with n = 8 using Simpson

Estimate the minimum number of subintervals needed to approximate the integral \int^4_2 \frac {1}{x -1} dx with an error of magnitude less than 10^{-4} using Simpson's Rule.

The reaction rate to a new drug is given by the following function where t is time (in hours) after the drug is administered. y = e^{-t^2} + \dfrac{7}{t + 7} a. Find the total reaction to the dru...

The table lists several measurements gathered in an experiment to

Use simpsons rule with n=4 to estimate the value of \frac {3dx}{\sqrt{(1+x)}} given a=1 and b=3.

Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve y = \ln(x), 1 \le x \le 3, about the x-axis.

Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis to six decimal places. y = ln(x) 4 greater than or equal to x less than or e...

Find an upper bound for the error in estimating \int_0^\pi {2x\cos \left( x \right)dx} using Simpson's rule with four steps.

Use "S" as the integral symbol 1) Find the integral f(x)=S(x^2-4x)^3(x-2)dx 2) Find the area (the same problem except the S has a 3 on top and a 1 on the bottom) 3) Find the area using the trapezoi...

Use Simpson's Rule with n = 4 steps to estimate the integral. \int_{-1}^{1}(x^{2}+7)dx

Given the following integral and value of, approximate the integral using the methods indicated (round your answers to six decimal places) (a) Trapezoidal Rule (b) Midpoint Rule (c) Simpson's Rule

Find SIMP(2) for the definite integral below. \int_{0}^{4}x^{2}dx

Estimate the area under the curve f (x) = square root x + 1 in the interval [0, 4] with n = 8 using Simpson's Rule.

Use Simpson s Rule to approximate the integral \int\limits_0^{1/2} \sin x^3 \text{ d}x with n=10 . Round your answer to 6 decimal places.

How large should n be to guarantee that the Simpson s Rule approximation to \int\limits_0^1 14e^{x^2} \text{ d}x is accurate to within 0.00001 ?

Estimate the given integral as defined by the provided data

It has been estimated that service industries, which currently make up 30% of the non-farm workforce in a certain country, will continue to grow at the rate of R(t)=8e^(1/(4t+7)) percent per decade...

Use Simpson's rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator. (Round your answer to six decimal places.) x...

What is Simpson's rule? How do you use it?

The integral 1=\int_{0}^{1}\frac{\sin x}{x}dx is important to design precise photographic lenses (among other applications) The function f(x)= \frac{\sin x}{x} however has no elementary antiderivat...

An electronics company analyst has determined that the rate per month t which revenue comes in from the portable GPS division is given by the following formula R(x)=110e^{0.04\sqrt{x}}+23 where x i...

State True or False and justify your answer: A high number for the Simpson's index of diversity indicates that there is a large diversity of species present in an ecosystem.

Use the simpson's rule with n=10 to estimate arc length of y=x^{-1/3}, for 1 \leq x <6.

When is right endpoint approximation more accurate than Simpson's rule?

How large should n be to guarantee that the Simpson's rule approximation to \int_{0}^{1}13ex^{2}dx is accurate to within 0.00001?

How large should n be to guarantee that the Simpson's rule approximation to \int \limits_0^1 3e^{x^2} dx is accurate to within 0.0001?

How large should n be to guarantee that the Simpson's rule approximation to integral^1_0 e^{x^2} dx is accurate to within 0.00001?

Using Simpson's Rule, calculate the integral integral^5_1 ({x^3}/{4} + x + 2) dx for n = 2.

The instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpson's rule. Complete part II. \int_{-\pi/2}^{\pi/2} 4 \cos t dt II. Using Simpson's rule complet...

The instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpson's rule. Complete part II. \int_{-\pi/2}^{\pi/2} 2 \cos t dt II. Using Simpson's rule complet...

can you please solve this CALCULUS question which is in the image below? thank you KEVEN

Use the method S(4)(Simpson's rule with n= 4) to approximate \int_{0}^{1/2}\frac{1}{1 + x^2}dx. Give the exact numerical expression. Do not combine the fractions into one term.

Approximate the following integral: \int \limits_1^5 x^3 dx, \ S_4. Additionally, determine the error.

Approximate the following integral: \int \limits_0^1 \arctan (x) dx, \ S_{12}. Additionally, determine the error.

Approximate the following integral: \int _0^{\sqrt{\pi}} \sin (x^2) dx, \ S_{20} Additionally, determine the error.

M_N give the exact area under the curve f(x)=6-x. f(x) is linear function. Determine the highest degree polynomial for which S_N gives the exact area. Explain Error (S_N) \leq \frac {k_4(b-a)^5}{18...

In the table below, letters represent species in a community; numbers indicate the number of individuals of each species in the community. Calculate Simpson's index of diversity for the community....

A car starts moving at time t=0 and goes faster and faster. Its velocity is shown in the following table. | t (seconds) | 0 | 3 | 6 | 9 | 12 | Velocity (ft/second) | 0 | 10 | 25 | 45 | 75 Estimate...

Find n such that the error in approximating the given definite integral \int_0^5 x^4 \ dx is less than 0.0001 when using: a. Trapezoidal Rule b. Simpson's Rule

Find n such that the error in approximating the given definite integral \int_1^4 \frac{1}{\sqrt x} \ dx is less than 0.0001 when using: a. Trapezoidal Rule b. Simpson's Rule

Find n such that the error in approximating the given definite integral is less than 0.0001 when using: a. Trapezoidal Rule b. Simpson's Rule \int_0^{\pi} \sin x \ dx

Recall from class the curve given by the intersection of the cylinder x^2 + y^2 = 2 and the plane x + z = 4. Use Simpson's Rule with n = 8 intervals to approximate the arc length of the curve r(t)...

Let I^M_n, , I^T_n, , I^S_n be the approximation of the definite integral I = \int_a^b f(x) dx calculated with midpoint rule, trapezoidal rule and Simpson's rule respectively, corresponding to a un...

Use Simpson's Rule and all the data in the following table to estimate the value of ? ? 10 ? 16 y d x x -16 -15 -14 -13 -12 -11 -10 y 0 -3 -9 9 -1 9 5

The following table gives the power consumption in megawatts for a region from midnight to 6:00 AM on a particular day. Use Simpson's Rule to estimate the energy used during this time period. (Roun...

The error function erf(x) = \frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2} dt important in probability and in the theories of heat flow and signal transmission, must be evaluated numerically because there i...

Approximate the area under the curve defined by the following data points. x 1 4 7 10 13 16 19 22 25 y 2 4.6 7 6.2 6 5.5 4 7.8 8

Use the error formula to find the smallest n such that the error int he approximation of the definite integral is less than 0.00001 using the following rules: a. The Trapezoidal Rule, b. Simpson's...

The table (supplied by San Diego Gas and Electric) gives the power consumption P in megawatts in San Diego County from midnight to 6:00 am on a day in December. Use Simpson's Rule to estimate the e...

Approximate the area under the curve defined by the following data points. x, 1,4,7,10,13,16,19,22,25

Find an approximate value for the integral, using Simpson's rule with n intervals.\\ \int_0^1 \frac{1}{1+x^2} dx, \ n=4 \\ A) 5323/6800 \\ B) 5323/3400 \\ C) 8011/10200 \\ D) 8011/5100

Given the error function erf[x] = \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} \, dt . Use Simpson's rule with n = 6 to find erf[3]

Find or evaluate the following indefinite and definite integral. \int \frac{x + 2}{\sqrt{4 - x^3}} dx

Using the error formula to estimate the errors in approximating the integral, with n = 8, using a) the Trapezoidal Rule and b) Simpson's Rule. \int^\frac{\pi}{3}_0 3\sin(2x)dx

Calculate the indicated Riemann sum S_5, for the function f(x) = 28 - 4 x^2. Partition [ - 1, 9] into five subintervals of equal length, and for each subinterval [x_{k - 1}, x_k], let C_K = (x_{k -...

Calculate the indicated Riemann sum S_4 for the function f(x) = 32 - 3 x^2. Partition [0, 12] into four subintervals of equal length, and for each subinterval [ x_{k - 1}, x_k ], let c_K = {2 x_{k...

Use Simpson rule with __n=10__ to approx the area of the surface obtained by rotating the curve about the X- axis.y=\frac {1}{5}x^5, \ \ 0 \leq x \leq 5\\ Simpson's \ Rule \ \ \Box\\ calculator \ a...

Use Simpson rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator. (Round your answer to six decimal places.) y =...

State whether the following statements are true or false and correct the false one: 1) Finite difference method is one of the integration methods. 2) Laplace equation covers all the engineering f...

A radar gun was used to record the speed of a runner during the first 5 seconds of a race. Use Simpson's rule to estimate the distance the runner covered during those 5 seconds | t (s) | 0 | 0.5 |...

For any pre-determined error bound, can you find an approximation with error smaller than that bound?

Use Simpson's rule and the data in the following table to estimate the value of \int_{27}^{33} y \, dx | x | 27 | 28 | 29 | 30 | 31 | 32 | 33 | y | -7 | -9 | -9 | -8 | -5 | -5 | 0

Approximate the following integral using the indicated methods. Round your answers to six decimal places. \int_{0}^{1} e^{-3x^2} \;dx (a) Trapezoidal Rule with 4 subintervals. (b) Midpoint Rule wi...

How large should n be to guarantee that the Simpson's Rule approximation to \int_0^1 e^{x^2} \, dx is accurate to within .00001 ?

Approximate the value of the integral defined by the given set of points. \int_{0}^{12} y \space dx (Give your answer to 2 decimal places.) HtmlTable <table><tr><th>x</th><th>0</th><th>2</th><th>4...

Use Simpson's rule with n = 4 to approximate. Keep at least 2 decimal places accuracy. \int_0^2 2/(x^2 + 1) dx

Evaluate the following integrals.(a) -1 to 2 integral square root 1+x^5 dx. (b) integral square root x+5 dx / x.

Find an n such that Simpson's S n is within 10 8 of 3 0 1 ( x + 2 ) d x . The error bound for Simpson's rule on int b a f ( x ) d x is M 4 ( b -a ) 5 / 180 n 4 , where M 4 is any...

A thin metal plate is shaped like a semicircle of radius 4 meters in the right half-plane, centered at the origin. The area density of the metal only depends on x x, and is given by an unknown func...

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) \int_1^5 \f...

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) \int_0^\frac{1}{2} 6 \s...

How large should n be to guarantee that the Simpson's Rule approximation to the integral from 0 to 1 of 9e^{x^2} dx is accurate to within 0.00001?

Find the smallest number of partitions n so that the approximation to integral 6 1 2 ln x d x using Simpson's Rule is accurate to within 0.0001?

The widths (in meters) of a kidney-shaped swimming pool were measured at 2-meter intervals as indicated in the figure. Using the trapezoidal rule and Simpson's rule, estimate the surface area of th...

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator. x = y + y^{1/2}, 1 less than or equal to y le...

Use Simpson's Rule to obtain your best approximation to the following integrals: I_3 = \int_0^{\pi/2} \cos ^7 x \ dx I_4 = \int_0^1 x^2 \ln^3 x \ dx

Approximate the following integrals using Simpson's Rule. Experiment with values of n to insure that the error is less than 10^{-6}. It is best to compute Simpson's Rule approximations and Trapezoi...

A radar gun was used to record the speed of a runner during the first three seconds of a race (see the table). Use Simpson's Rule to estimate the distance the runner covered during those three seco...

Use Simpson's Rule with n = 6 to estimate the arc length of the curve, L. Give your answer to six decimal places. x=y +\sqrt y, \ 2 \leq y \leq 5

Using a numerical technique, discuss the merits of the Midpoint Rule, Trapezoid Rule, and Simpon's Rule. Which methods give better (more precise) approximations? Why?

Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator. (Round your answers to six decimal places.) y =...

The following table shows the rate of water flow (in L/min) through a dam. Approximate the total volume of water that passed through the dam from

How large should n be to guarantee the Simpson's Rule approximation to \int _0^1 e^{x^2} \ dx is accurate to within 0.00001?

Find the indefinite integral \int \frac {(\frac {5^3}{x} - (x^8 + 9)^{1/3} )}{ 3x^2} dx

The area of a meadow was approximated by measuring the length of the meadow at 30-foot intervals. THe distances measured across the meadow were 76 ft, 118 ft, 130 ft, 143 ft, 139 ft, 136 ft, 137 ft...

Use the Trapezoidal and Simpson's rule to approximate the value of the definite integral? \int _1^6 5(x^2-1) dx, n=4. Compare your result with the exact value of the integral. (Give your answers c...

f(1)= 20, f(3)=13, f(5)=15, f(7)=16, f(9)=11, on ~0,6 a. used midpint rule with n=5 to estimate { \int_0^{10} f(x)dx } b, use trapezoidal rule with n=4 to estimate { \int_0^9 f(x)dx } c, used...

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. y = tan x, 0 less than x less than pi / 9.

Calculate the integral of: \int \frac{(x^2)\tan(x)}{1+\cos(x)^4}dx

How large should n be to guarantee that the Simpsons rule approximation to integral 0 to 1 7 e^x^2 is accurate to with in 0.00001?

Use Simpson's rule with n = 4 to approximate integral_1^5 {cos x} / x dx.

The table below gives the power consumption in megawatts in Hartford County from midnight to 3:00 A.M. on a day in December. Use Simpson's Rule to estimate the energy used during that time period....

A radar gun was used to record the speed of a runner during the first 5 seconds of a race (see table). Use Simpson's rule to estimate the distance the runner covered during those 5 seconds. |t(s)...

The planet Pluto travels in an elliptical orbit around the Sun (at one focus). The length of the major axis is 1.18 \times 10^{10} km and the length of the minor axis is 1.14 \times 10^{10} km. Use...

Find the Error resulted from approximation by Simpson's Rule: { \int_0^1 \sqrt{( 1+x^3)} dx } compute the result for n = 8

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) the Simpson Rule to approximate the integral \int_{0}^{1}x^3\ dx; n=6. Round your answers to six decimal places.

Use Simpson's Rule with n = 6 to estimate the length of the curve x = t - e^t, y = t + e^t, - 6 less than or equal to t less than or equal to 6.

The widths (in meters) of a kidney-shaped swimming pool were measured at 7-meter intervals as indicated in the figure. Use the Midpoint Rule with n = 4 to estimate the area S of the pool if a_1 = 1...

Use Simpson?s Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator. y = x \sin x, 0 \leq x \leq 2\pi.

How large should be to guarantee that the Simpson's Rule approximation to integral_0^1 e^{x^2} dx is accurate to within 0.00001?

The area a meadow was approximated by measuring the length of the meadow at 30 foot intervals. The distances measured across the meadow were 76 ft, 118 ft, 130 ft, 143 ft, 139 ft, 136 ft, 137 ft, 1...

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator. x = y + y^{1/2}, 1 less than or equal to y le...

Sketch the graph of a continuous function on (0, 2) for which the Trapezoidal Rule with n = 2 is more accurate than the Midpoint Rule.

Suppose you are asked to estimate the volume of a football. You measure and find that a football is 28 cm long. You use a piece of string and measure the circumference at its widest point to be 53...

Estimate the area under the graph in the figure by using a. Trapezoidal Rule b. The Midpoint Rule c. Simpson's Rule each with n = 4. (Graph)

Calculate the maximum possible error associated with each estimate below. int_0^1 sin(x^2)/1+xdx. The two graphs show the second and fourth derivatives of sin(x^2)/1+x on the interval [0,1]. a....

Evaluate Integral integral_2^{10} 2 / s^2 ds using the trapezoidal rule and Simpson's rule. Determine i. the value of the integral directly. ii. the trapezoidal rule estimate for n = 4. iii. an up...

Consider the graph. a. If f(x) = sin (sin x) use this graph to find an upper bound for |f^{(4)}(x)|. b. Use Simpson's Rule with n = 10 to approximate

The design of a new airplane requires a gasoline tank of constant cross-section in each wing. The tank must hold 5000 lb. of gasoline that weighs 42 lb/ft^3. a. A scale drawing of a cross-section...

A town wants to drain and fill a small polluted swamp. The swamp is approximately 5 feet deep. Measurements were taken across the swamp at 20-foot intervals. About how many cubic yards of dirt will...

Find: Use Simpson's method with n=4 to approximate \int_0^8 f(x) dx where y=f(x) is given by the graph below. Image src='img_22082019_202247_448_x_500_pixel5654188452921282223.jpg' alt='' caption=''

The dimensions, in inches of a streamlined strut are shown in the figure below. Approximate the cross-sectional area using 1. Trapezoidal Rule 2. Simpson's Rule

Locate the centroid \bar{y} of the shaded area. Solve the problem by evaluating the integrals using Simpson's rule.

Find: Estimate the area between x=0 and x=4 under the graph in the figure by using a) the Trapezoidal Rule b) the Midpoint Rule c) Simpson's Rule each with n = 4. What observations c...

The velocity v ( t ) ft/sec of an object moving on the x -axis at t sec is recorded as t 2.0 2.25 2.50 2.75 3.0 3.25 3.5 3.75 4.0 v(t) 5.21 6.14 7.24 6.79 6.15 5.89 5.96 6.18 9.89 Using Simps...

The table shows values of a force function f(x), where x is measured in meters and f(x) in newtons. Use Simpon's Rule to estimate the work done by the force in moving an object a distance of 18 m.

Use the inequalities |E_M|= |integral_a^b f(x) dx - M_n| less than or equal to (b-a)^3 K_2 / 24n^2 |E_T|= |integral_a^b f(x) dx - T_n| less than or equal to (b-a)^3 K_2 / 12n^2 |E_S|= |integra...

Here are four ways to compute Definite Integrals. Show two or three more ways like these to compute definite integrals. integral_{x_0}^{x_n} f(x) dx approx h Sigma_{i=0}^{n-1} f(x_i) integral_{x_0}...

Miguel is traveling in a car with a broken odometer. To approximate the distance he travels in one hour, he takes a speedometer reading every 10 minutes. \begin{array}{|l|l|l|l|l|l|l|l|} \hline Min...

Students are required to calculate the drag coefficient C D of the fluid flow across a circular cylinder. The formula for calculating C D is given as: C D = ? ? 0 C p cos ? d ? . " C p cos (...

Let f(x)=100 (x-1)^3e^{-x^2} . Approximate the value of the integral \int_{0.6}^{1.5} f(x) \, dx

Evaluate \int^{14}_0 x\sqrt{196-x^2}\;dx. Then, using the tabulated values, apply the Trapezoidal Rule and Simpson's Rule to obtain estimates of the value. Determine i. the value of the integral di...

The function f(x)=e^-x can be used to generate the following table of unequally spaced data: Evaluate the integral from a=0 to b=0.6 using: (a) analytical means, (b) the trapezoidal rule, (c) a...

(a) Use Simpson's Rule, with n=6, to approximate the integral integral_0^1 8e^{-3x} dx. S_6= (b) The actual value of integral_0^1 8e ^{-3x} dx= (c) The error involved in the approximation of part (...

We often need to use numerical integration when we cannot apply the Fundamental Theorem of Calculus. Let us investigate \int_{0}^{2}\sqrt{1 + 9x^4}dx, an integral that we cannot do exactly in the c...

Water leaks from a tank at a rate r ( t ) gallons per hour. Estimate the total amount of water that leaks out during the first four hours, using... t 0 0.5 1 1.5 2 2.5 3 3.5 4 r(t) 4.00 2.82 2.1...

Consider the area shown in (Figure 1) . Suppose that x0 = 1.2 m . Locate the centroid \bar{y} of the shaded area. Solve the problem by evaluating the integrals using Simpson's rule \int_b^af(x)d...

1. Evaluate the integral below using the trapezoidal rule. Use sub-interval widths of 1, 0.5, and 0.25, and compare your results with the true value of I=-0.346078. 2. Evaluate the integral below u...

Approximate \ln 5 by choosing the appropriate value of b and approximate the integral below by Simpson's Rule with n=8 Be sure to render your final approximation as a decimal after displaying your...

Given integral_{-9}^{9}(-3x^4+5x-9)dx a) Compute the exact values using Fundamental Theorem of Calculus. b) Find the approximate value of the definite integral using the trapezoidal rule with n=9 c...

Find the smallest number of partitions n so that the approximation \int_{1}^{8} 2 In xdx using Simpson's Rule is accurate to within 0.0001.

Approximate F(x) for x = 0, 0.5, 1, 1.5, 2, 2.5. F(x) = \int^x_0\sin(t^2)dt Round your answers to three decimal places. F(0) = _____ F(0.5) = _____ F(1) = _____ F(1.5) = _____ F(2) = _____ F(2...

Find the integral: \int \frac{dx}{\sqrt{9+8x^2-x^4}}

Use Simpson's rule to approximate \int_{0}^{\pi}\sin(x)dx with n= 4.

The widths (in meters) of a kidney-shaped swimming pool, measured at 2-meter intervals, are: 0,4.4,5.3,6.2,7.7,6.3, and 0. Use Simpson's Rule to estimate the area of the pool.

Integrate (lim: 0 to 2pi) 2 s i n^x e^x d x Using the integral above, approximate the area using the Trapezoid rule with 4 subdivisions, and the Simpson's Rule with 4 subdivisions.

Use Simpson's Rule to approximate the value of the definite integral integral_0^8 2^4 sqrt x dx with n=8.

A surveyor measured the length of a piece of land at 100-ft intervals (x), as shown in the table. Use Simpson's Rule to estimate the area of the piece of land in square feet. x Length (ft) 0 50...

Use n=4 and Simpson's Rule to approximate the integral \int_{0}^{2} e^{x^2} dx

Use Simpson's Rule with N = 6 to approximate the value of the following integral. integral_1^3 1 / x^2 d x approx ?

Find: Use Simpson's rule with either n=5 or n=6 (only one of these is appropriate, choose the correct one ) to approximate \int_0^3 \frac{1}{9+x^2} dx to four places after the decimal.

Evaluate the integral. \displaystyle\int _ { 0 } ^ { 1 } x ^ { 2.5 } \sqrt { ( 2.5 x ^ { 1.5 } ) ^ { 2 } + 1 } d x

Use Simpson's Rule with n= 10 to estimate the arc length of the curve y = \ln(7 + x^3), 0 less than or equal to x less than or equal to 5. Compare your answer with the value of the integral produce...

Evaluate the definite integral. I am supposed to do it with substitution but don't know what to substitute for this problem. \int^4_1 ( \frac {e^{4x} }{ x^2} ) dx

{ f(x) = \sqrt{\frac{5}{x}} + 2 } use sympson's rule with N=6 to evaluate the integral of the following function over x& ~1,2

Find the smallest number of partitions "n" so that the approximation to integral 3lnx dx (with boundaries a = 1 and b = 7) using Simpson's Rule is accurate to within 0.0001?

Use Simpson's rule to approximate \int_0^4 x^3 \, dx with n = 8.