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: 5


$\frac{81 \pi}{10}.$

Work Step by Step

The volume of revolution is given by $$ \pi \int_{0}^{3}\left(3 x-x^{2}\right)^{2} d x=\pi \int_{0}^{3}\left(x^{4}-6 x^{3}+9 x^{2}\right) d x\\=\left.\pi\left(\frac{1}{5} x^{5}-\frac{3}{2} x^{4}+3 x^{3}\right)\right|_{0} ^{3}=\frac{81 \pi}{10}. $$
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