   Chapter 5.3, Problem 43E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Evaluate the integral. ∫ 0 π f ( x )   d x where   f ( x ) = { sin x if 0 ≤ x < π / 2 cos x if π / 2 ≤ x ≤ π

To determine

To evaluate: The integral function 0πf(x)dx.

Explanation

Given:

The integral function is 0πf(x)dx.

Here, f(x) is function of x.

Express the function f(x) as shown below:

f(x)={sinx if 0x<π2cosx if π/2xπ (1)

Calculation:

Modify Equation (1) as follows:

0πf(x)dx=0π2sinxdx+π2πcosxdx (2)

Integrate Equation (2) with respect to x and apply the upper and lower limits

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

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Study Guide for Stewart's Multivariable Calculus, 8th 