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: 32


$12 \pi \ \approx 38 \mathrm{grams}.$

Work Step by Step

The total mass is given by $$ 2 \pi \int_{0}^{20} r \rho(r) d r=2 \pi \int_{0}^{20}\left(0.03 r+0.01 r \cos \left(\pi r^{2}\right)\right) d r=\left.2 \pi\left(0.015 r^{2}+\frac{0.01}{2 \pi} \sin \left(\pi r^{2}\right)\right)\right|_{0} ^{20}=12 \pi \ \mathrm{grams}. $$
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