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 383: 40



Work Step by Step

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