Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 16 - Vector Calculus - 16.9 The Divergence Theorem - 16.9 Exercises - Page 1185: 2


$2430 \pi$

Work Step by Step

$I=\iiint_Ediv \overrightarrow{F}dV =\int_0^{2 \pi}\int_0^3\int_{r^2}^{0} (10 z) r dz dr d\theta $ $=\int_0^{2 \pi}\int_0^3 [5z^2 r]_{r^2}^0 dr d\theta $ $=\int_0^{2 \pi}\int_0^3 405r-5r^5 dr d\theta $ $=\int_0^{2 \pi}[(\dfrac{405r^2}{2}-\dfrac{5r^6}{6}))]_0^3 d\theta $ $=\int_0^{2 \pi} \dfrac{405(3)^2}{2}-\dfrac{5 \cdot 3^{6}}{6} d\theta $ $=\int_0^{2 \pi} 1215 d \theta $ $=2430 \pi$
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