   Chapter 7.7, Problem 6E

Chapter
Section
Textbook Problem

# 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 value to determine the error in each approximation. ∫ 0 π x cos x   d x , n = 4

To determine

(a)

To find: Approximate integral using the midpoint rule

Explanation

Given: f(x)=xcosx,n=4,a=0,b=πΔx=ban=π4

Formula used: M4=0πxcosxdxΔx[f(x0)+f(x1)+f(x2)+f(x3)]

For the midpoint rule, calculate values for the function at the middle of each interval. So we start at x=π8 and increment by Δx

To determine

(b)

To find: Approximate integral using the Simpson’s rule

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