Calculus 8th Edition

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

Chapter 5 - Applications of Integration - 5.2 Volumes - 5.2 Exercises - Page 375: 24


$\displaystyle{V=\frac{\pi}{9} }$

Work Step by Step

$\displaystyle{y=\sqrt[4] x}\\ \displaystyle{x=y^4}$ $\displaystyle{A(y)=\pi\left(y^4\right)^2}\\ \displaystyle{A(y)=\pi\left(y^8\right)}$ $\begin{aligned} V &=\int_{0}^{1} A(y) \ d y \\ V &=\int_{0}^{1} \pi\left(y^8\right) \ d y \\ V &=\pi \int_{0}^{1} y^8\ dy \\ V &=\pi\left[\frac{1}{9} x^9\right]_{0}^{1} \\ V &=\pi\left(\left(\frac{1}{9} (1)^9\right)-(0)\right) \\ V &=\frac{\pi}{9} \end{aligned}$
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.