Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 6 - Applications of the Integral - 6.3 Volumes of Revolution - Exercises - Page 304: 8


$\frac{256 \pi}{15}.$

Work Step by Step

The volume is given by $$ \pi \int_{0}^{2}\left(4-x^{2}\right)^{2} d x=\pi \int_{0}^{2}\left(16-8 x^{2}+x^{4}\right) d x\\=\left.\pi\left(16 x-\frac{8}{3} x^{3}+\frac{1}{5} x^{5}\right)\right|_{0} ^{2}=\frac{256 \pi}{15}. $$
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