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: 28

Answer

$$\int e^{\cos t}\sin tdt=-e^{\cos t}+C$$

Work Step by Step

$$A=\int e^{\cos t}\sin tdt$$ Let $u=\cos t$. We would have $du=-\sin tdt$. Therefore, $\sin tdt=-du$ Substitute into $A$, we have $$A=-\int e^udu$$ $$A=-e^u+C$$ $$A=-e^{\cos t}+C$$
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.