   Chapter 5.5, Problem 51E ### 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 indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take C = 0). ∫ e cos x sin x   d x

To determine

To evaluate: The indefinite integral ecosxsinxdx

Explanation

Given:

The indefinite integral function is ecosxsinxdx.

Calculation:

Consider u=cosx

Differentiate both sides of the equation.

du=sinxdxdu=sinxdx

The indefinite integral function is,

ecosxsinxdx (1)

Substitute u for (cosx) and (du) for (sinxdx) in Equation (1).

ecosxsinxdx=eu(du)=eudu (2)

Integrate Equation (2)

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