Question

Consider the following integral: \int_0^2 \frac{8}{x^2 + 4}dx (a) Use MatLab to find the value of the definite integral numerically using Riemann Sums. First, write down ALL the commands to compute the integral using 10 rectangles. What is the value of the integral. (b) Recompute the sum using 100 rectangles. (c) Recompute the sum using 1000 rectangles. (d) What value does sum converge to as $n \to \infty$?

          Consider the following integral:
\int_0^2 \frac{8}{x^2 + 4}dx
(a) Use MatLab to find the value of the definite integral numerically using Riemann Sums.
First, write down ALL the commands to compute the integral using 10 rectangles. What
is the value of the integral.
(b) Recompute the sum using 100 rectangles.
(c) Recompute the sum using 1000 rectangles.
(d) What value does sum converge to as $n \to \infty$?

Consider the following integral:
∫0^2 (8)/(x^2 + 4)dx
(a) Use MatLab to find the value of the definite integral numerically using Riemann Sums.
First, write down ALL the commands to compute the integral using 10 rectangles. What
is the value of the integral.
(b) Recompute the sum using 100 rectangles.
(c) Recompute the sum using 1000 rectangles.
(d) What value does sum converge to as n →∞?

Added by Devin P.

Calculus for Scientists and Engineers: Early Transcendental

William Briggs, Lyle Cochran, Bernard… 1st Edition

Chapter 5

Instant Answer

Solved by Expert Robert Fox

Step 1

The formula for the Riemann sum is: Riemann sum = ∑(f(xi) * Δx) where f(xi) is the value of the function at the midpoint of each rectangle, and Δx is the width of each rectangle. In this case, we need to find the integral of a function numerically, so we need Show more…

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Consider the following integral: (a) Use MatLab to find the value of the definite integral numerically using Riemann Sums First, write down ALL the commands to compute the integral using 10 rectangles. What is the value of the integral. (b) Recompute the sum using 100 rectangles. (c) Recompute the sum using 1000 rectangles (d) What value does sum converge to as n - o?