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 16.3 - Path Independence, Conservative Fields, and Potential Functions - Exercises 16.3 - Page 966: 10


$$ f=y \space x \sin (z)+c $$

Work Step by Step

We have $$ f=y \space x \sin (z) +g(y,z)$$ and $$ g(y,z)=0 \implies g(y,z)=h(z)=0$$ So, $ f=y \space x \sin z+h(z)$ Now, $ f_z=yx \cos z+h'(z)=yx \cos z $ So, $$ f=y \space x \sin (z)+c $$
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