University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 8 - Section 8.5 - Integral Tables and Computer Algebra Systems - Exercises - Page 451: 23



Work Step by Step

$$A=\int8\sin4t\sin\frac{t}{2}dt$$ Use Formula 69b, which states that $$\int \sin ax\sin bx dx=\frac{\sin(a-b)x}{2(a-b)}-\frac{\sin(a+b)x}{2(a+b)}+C$$ for $a=4$ and $b=1/2$: $$A=8\Big(\frac{\sin\frac{7}{2}t}{2\times\frac{7}{2}}-\frac{\sin\frac{9}{2}t}{2\times\frac{9}{2}}\Big)+C$$ $$A=8\Big(\frac{\sin\frac{7}{2}t}{7}-\frac{\sin\frac{9}{2}t}{9}\Big)+C$$ $$A=\frac{8}{7}\sin\frac{7}{2}t-\frac{8}{9}\sin\frac{9}{2}t+C$$
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.