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: 10



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 $$ Flux =\iiint_{o} 12x+12y+2 \space dz \space dy \space dx \\=\nabla \cdot F \\=\int_{0}^{3}\int_{0}^{\pi/2}\int_{0}^{2} (12r \cos \theta+2r \sin \theta +2) \space dr \space d\theta dz \\=\int_{0}^{3}(32+2\pi+\dfrac{16}{3}) \space dz \\=6\pi+112$$
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