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


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

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 $$A=-\int e^udu$$ $$A=-e^u+C$$ $$A=-e^{\cos t}+C$$
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