Answer
$=\frac{16\pi}{3}$
Work Step by Step
Setup the integration using shell method about the x-axis
$2\pi\int_{2}^0 y(y^2-2-y)$
$=2\pi\int_{2}^0 (y^3-y^2-2y)$
$=2\pi[\frac{y^4}{4}-\frac{y^3}{3}-y^2]_2^0$
$=\frac{16\pi}{3}$
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 7 - Applications of Integration - 7.3 Exercises - Page 462: 22
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