Calculus (3rd Edition)

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

Chapter 6 - Applications of the Integral - 6.2 Setting Up Integrals: Volume, Density, Average Value - Exercises - Page 298: 30



Work Step by Step

The number of gorillas is given as follows $$ 2 \pi \int_{0}^{5} r \rho(r) d r=\int_{0}^{5} \frac{104 \pi r}{\left(1+r^{2}\right)^{2}}dr\\ =\int_{0}^{5} 104 \pi r \left(1+r^{2}\right)^{-2}dr=-\left.\frac{52 \pi}{1+r^{2}}\right|_{0} ^{5}=50 \pi\approx 157. $$
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