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


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

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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 ...

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Learn more about this topic:

How to Use Riemann Sums to Calculate Integrals


Chapter 12 / Lesson 7

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.

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