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: 36


$112.09\ \ \mathrm{cm}^{3}/\mathrm{s}$

Work Step by Step

The flow rate is given by $$ \begin{aligned} 2 \pi \int_{0}^{2} r v(r) d r &=2 \pi \int_{0}^{2} r\left(10-0.3 r-0.34 r^{2}\right) d r\\ &=2 \pi \int_{0}^{2}\left(10 r-0.3 r^{2}-0.34 r^{3}\right) d r \\ &=\left.2 \pi\left(5 r^{2}-0.1 r^{3}-0.085 r^{4}\right)\right|_{0} ^{2} \\ &=112.09\ \ \mathrm{cm}^{3}/\mathrm{s} \end{aligned} $$
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