Answer
$yx+zx+zy+C$
Work Step by Step
Consider $f(x,y,z)=yx+zx+g(y,z)$
Also, $\nabla f =F$
and $g_y(y,z)=z$
Then, $g(y,z)=zy+h(z)$ and $h(z)=C$
$f(x,y,z)=yx+zx+zy+h(z)$
Thus, $f(x,y,z)=yx+zx+zy+C$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 16: Integrals and Vector Fields - Section 16.3 - Path Independence, Conservative Fields, and Potential Functions - Exercises 16.3 - Page 966: 8
Update this answer!
You can help us out by revising, improving and updating this answer.
Update this answerAfter 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.
