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: 6


$\frac{21 \pi}{64}$

Work Step by Step

The volume is given by $$ \pi \int_{1}^{4}\left(x^{-2}\right)^{2} d x=\pi \int_{1}^{4} x^{-4} d x=-\frac{\pi}{3} x^{-3}|_{1} ^{4}=\frac{21 \pi}{64}. $$
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