Calculus 8th Edition

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

Chapter 4 - Integrals - Review - Exercises - Page 349: 17



Work Step by Step

Given $$\int_0^1y(1+y^2)^5dy$$ Let $u=1+y^2\ \Rightarrow \ \ du=2ydy$ at $ y=0\to u=1$,at $ y=1\to u=2$ \begin{align*} \int_0^1y(1+y^2)^5dy&=\frac{1}{2}\int_1^2u^5du\\ &=\frac{1}{12}u^6\bigg|_{1}^{2}\\ &=\frac{63}{12}=\frac{21}{4} \end{align*}
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