Copyright

Find R5 for f(x) = {eq}x^2 + 2x {/eq} on {eq}[0,10] {/eq}.

Question:

Find R5 for f(x) = {eq}x^2 + 2x {/eq} on {eq}[0,10] {/eq}.

Numerical Integration:

The definite integral of a function {eq}f(x) {/eq} over the interval {eq}[x_0,x_1] {/eq} can be approximated by a Riemann sum.

The interval is divided into subdomains {eq}[x_{n-1}, x_n] {/eq}

and the integral is approximated by the right Riemann sum

{eq}\displaystyle R = \sum_{n} f(x_{n})\Delta {/eq}

where {eq}\Delta {/eq} is the width of each subdomain.

Answer and Explanation: 1

Become a Study.com member to unlock this answer!

View this answer

We are given

{eq}x_0 =0 \\ x_1 = 10 \\ f(x) =x^2 + 2x {/eq}

The interval between {eq}[0,10] {/eq} is divided into 5 intervals of equal width ...

See full answer below.


Learn more about this topic:

Loading...
How to Use Riemann Sums to Calculate Integrals

from

Chapter 12 / Lesson 7
10K

Riemann sums use the method of 'slicing' the area of a graph to isolate the equation used to calculate definite integrals. Follow example problems of using Riemann sums to find an area even when divided into different sections.


Related to this Question

Explore our homework questions and answers library