Answer
$\frac{\pi}{5}$
Work Step by Step
$$ V = \pi \int_{0}^{1}[{(1-x^2)}^2-{(1-x)}^2]dx$$
$$ V = \pi \int_{0}^{1}[2x-3x^2+x^4]dx$$
$$ V = \pi [x^2-x^3+\frac{x^5}{5}]_{0}^{1}dx$$
$$ V = \pi[\frac{1}{5}]=\frac{\pi}{5}$$
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 - 7.2 Exercises - Page 454: 44
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