Calculus 8th Edition

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

Chapter 5 - Applications of Integration - 5.3 Volumes by Cylindrical Shells - 5.3 Exercises - Page 382: 10



Work Step by Step

$\displaystyle{V=\int_{0}^{2}(2\pi y)\left(y^2\right)\ dy}\\ \displaystyle{V=2\pi\int_{0}^{2}y^3\ dy}\\ \displaystyle{V=2\pi\left[\frac{1}{4}y^4\right]_{0}^{2}}\\ \displaystyle{V=2\pi\left(\left(\frac{1}{4}(2)^4\right)-(0)\right)}\\ \displaystyle{V=8\pi}\\$
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