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: 4

Answer

$$\int \sin^2\theta\cos\theta d\theta=\frac{\sin^3\theta}{3}+C$$

Work Step by Step

$$A=\int \sin^2\theta\cos\theta d\theta$$ Let $u=\sin\theta$ Then $du=(\sin\theta)'d\theta=\cos\theta d\theta$. Substitute into $A$, we have $$A=\int u^2du$$ $$A=\frac{u^3}{3}+C$$ $$A=\frac{\sin^3\theta}{3}+C$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.