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: 9


$$3\pi $$

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 $$ Flux =\iiint_{o} 3x \space dz \space dy \space dx\\=\int_{0}^{\pi/2}\int_{0}^{\pi/2}\int_{0}^{2} (3 \rho \sin \phi \space \cos \theta) \times (\rho^2 \sin \phi) \space d\rho \space \space d\phi \space d\theta\\= \int_{0}^{\pi/2}(3\pi \cos \theta) d\theta \\= 3\pi $$
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