University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 15 - Section 15.8 - The Divergence Theorem and a Unified Theory - Exercises - Page 906: 8


$32 \pi$

Work Step by Step

As we know that $div F=\dfrac{\partial A}{\partial x}i+\dfrac{\partial B}{\partial y}j+\dfrac{\partial C}{\partial z}k$ Now, we have $Flux =\iiint_{o}(2x+3) dz dy dx$ Also, $Flux =\nabla \cdot F=\int_{0}^{2\pi}\int_{0}^{\pi}\int_{0}^{2} (2 \rho \sin \phi \cos \theta+3)(\rho^2 \sin \phi) d\rho d\phi d\theta$ This implies that $\int_{0}^{2 \pi}(4 \pi \cos \theta +16) d\theta = 32 \pi$
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