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: 7


$$ -8 \pi $$

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 $ From the given equation, we have $$ Flux =\iiint_{o}(x-1) dz dy dx \\ =\nabla \cdot F=\int_{0}^{2\pi}\int_{0}^{2}\int_{0}^{r^2} (r \cos \theta-1) \space dz \space dr \space d\theta\\=\int_{0}^{2 \pi}(\dfrac{32}{5}\times \cos \theta -4) d\theta \\= -8 \pi $$
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