   Chapter 7.7, Problem 3E

Chapter
Section
Textbook Problem

# Estimate ∫ 0 1 cos ( x 2 )   d x using (a) the Trapezoidal Rule and (b) the Midpoint Rule, each with n = 4 . From a graph of the integrand, decide whether your answers are underestimates or overestimates. What can you conclude about the true value of the integral?

To determine

(a)

To find: Approximate integral using trapezoidal rule

Explanation

Formula used:

Tn=Δx2[f(x0)+i=1n1f(xi)+f(xn)]

Given:

f(x)=cos(x2),a=0,b=1,n=4Δx=ban=14

The intervals are [0,1/4],[1/4,1/2],[1/2,3/4],[3/4,1]

To determine

(b)

To find: Approximated integral using midpoint rule

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