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: 7


$ -8 \pi$

Work Step by Step

As we know that $div F=\dfrac{\partial A}{\partial x}i+\dfrac{\partial B}{\partial y}j+\dfrac{\partial C}{\partial z}k$ Now, we have $Flux =\iiint_{o}(x-1) dz dy dx$ Also, $Flux =\nabla \cdot F=\int_{0}^{2\pi}\int_{0}^{2}\int_{0}^{r^2} (r \cos \theta-1) dz dr d\theta$ This implies that $\int_{0}^{2 \pi}(\dfrac{32}{5} \cos \theta -4) d\theta = -8 \pi$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.