   Chapter 5, Problem 29RE ### 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, if it exists. ∫ sin π t cos π t   d t

To determine

To evaluate: The value of the integral.

Explanation

Given:

The integral function is sinπtcosπtdt.

Consider sinπt as u.

u=sinπt (1)

Differentiate both sides of the Equation.

du=(cosπt×π)dt=πcosπtdt (2)

Rearrange Equation (2) to find the value of cosπtdt as shown below:

cosπtdt=1πdu (3)

Substitute u for sinπt and 1πdu for cosπtdt in the function as follows

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