Answer
$\frac{8\pi}{3}$
Work Step by Step
Setup the integration using shell method about the x-axis
$2\pi \int_0^2 y(2-y)dy$
$ 2\pi \int_0^2 (2y-y^2)dy$ , Integrate
$2\pi (y^2 -\frac{1}{3}y^3)]_0^2$
$2\pi(4-\frac{8}{3})$
$\frac{8\pi}{3}$
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: 15
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