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: 15



Work Step by Step

$\displaystyle{x^3=8}\\ x=2$ $\displaystyle{V=\int_{0}^{2}(2\pi (3-x))\left(8-x^3\right)\ dx}\\ \displaystyle{V=2\pi\int_{0}^{2}x^4-3x^3-8x+24\ dx}\\ \displaystyle{V=2\pi\left[\frac{1}{5}x^5-\frac{3}{4}x^4-4x^2+24x\right]_{0}^{2}}\\ \displaystyle{V=2\pi\left(\left(\frac{1}{5}(2)^5-\frac{3}{4}(2)^4-4(2)^2+24(2)\right)-(0)\right)}\\ \displaystyle{V=\frac{264\pi}{5}}$
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