Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 16: Integrals and Vector Fields - Section 16.8 - The Divergence Theorem and a Unified Theory - Exercises 16.8 - Page 1025: 8


$$= 32 \pi $$

Work Step by Step

We know that $$ div F=\dfrac{\partial P}{\partial x}i+\dfrac{\partial Q}{\partial y}j $$ From the given equation, we have $$ Flux =\iiint_{o}(2x+3) \space dz \space dy \space dx \\ =\nabla \cdot F \\=\int_{0}^{2\pi}\int_{0}^{\pi}\int_{0}^{2} (2 \rho \sin \phi \cos \theta+3) \space (\rho^2 \sin \phi) \space d\rho \space d\phi \space d\theta \\ =\int_{0}^{2 \pi}(4 \pi \cos \theta +16) d\theta \\= 32 \pi $$
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