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 16.6 - Surface Integrals - Exercises 16.6 - Page 1001: 32



Work Step by Step

We have: $n=\dfrac{2xi+2yj+2z k}{2 \sqrt {x^2+y^2+z^2}}=\dfrac{xi+yj+z k}{a}$ Thus, $F \cdot n=\dfrac{-x}{a}+\dfrac{-x}{a}$ and $d \theta=\dfrac{2a}{2z} \ dA$ We set up the integral and solve the flux of $F$ as follows: $\iint_{S} F \cdot n \ d \theta =\iint_{R} (\dfrac{-x}{a}+\dfrac{-x}{a}) (\dfrac{2a}{2z}) \ dA$ or, $=\iint_{R} (0) (\dfrac{a}{z}) \ dA$ or, $=\iint_{R} (0) \ dA$ or, $=0$
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.