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 374: 6


$\displaystyle{V=\frac{256\pi }{5}}\\ $

Work Step by Step

$\displaystyle{2x=y^2}\\ \displaystyle{x=\frac{y^2}{2}}$ $\displaystyle{A\left(y\right)=\pi \left(\frac{y^2}{2}\right)^2}\\ \displaystyle{A\left(y\right)=\pi \left(\frac{y^4}{4}\right)}\\$ $\displaystyle{V=\int_0^4A\left(y\right)\ dy}\\ \displaystyle{V=\int_0^4\pi \left(\frac{y^4}{4}\right)\ dy}\\ \displaystyle{V=\frac{\pi}{4}\int_0^4y^4\ dy}\\ \displaystyle{V=\frac{\pi}{4}\left[\frac{1}{5}y^5\right]_0^4}\\ \displaystyle{V=\frac{\pi}{4}\left(\left(\frac{1}{5}\times4^5\right)-\left(\frac{1}{5}\times0^5\right)\right)}\\ \displaystyle{V=\frac{256\pi }{5}}\\ $
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