Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 5 - Section 5.5 - The Substitution Rule - 5.5 Exercises - Page 419: 15


$$\int\cos^3\theta\sin\theta d\theta=-\frac{\cos^4\theta}{4}+C$$

Work Step by Step

$$A=\int\cos^3\theta\sin\theta d\theta$$ Let $u=\cos\theta$. Then $du=-\sin\theta d\theta$, so $\sin\theta d\theta=-du$ Substitute into $A$, we have $$A=-\int u^3du$$ $$A=-\frac{u^4}{4}+C$$ $$A=-\frac{\cos^4\theta}{4}+C$$
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