Calculus 8th Edition

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

Chapter 4 - Integrals - Review - Exercises - Page 349: 21


$$\frac{1}{3}\sin \left(1\right)$$

Work Step by Step

Given $$\int_{0}^{1}v^2\cos(v^3)dv$$ Let $x=v^3\ \Rightarrow \ dx=3v^2dv $, at $v=0\to x=0$, at $v=1\to x=1$, then \begin{align*} \int_{0}^{1}v^2\cos(v^3)dv&=\frac{1}{3}\int_{0}^{1}\cos(x)dx\\ &=\frac{1}{3}\sin x\bigg|_{0}^{1}\\ &=\frac{1}{3}\sin \left(1\right) \end{align*}
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