Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 4 - Integrals - Review - Exercises - Page 349: 20


$$\frac{2}{3\pi }$$

Work Step by Step

Given $$\int_{0}^{1}\sin(3\pi t)dt$$ Let $x=3\pi t\ \Rightarrow \ dx=3\pi dt $, at $t=0\to x=0$, at $t=1\to x=3\pi$, then \begin{align*} \int_{0}^{1}\sin(3\pi t)dt&=\frac{1}{3\pi}\int_{0}^{3\pi}\sin(x)dx\\ &=\frac{-1}{3\pi}\cos x\bigg|_{0}^{3\pi}\\ &=\frac{2}{3\pi } \end{align*}
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.