Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 16 - Vector Calculus - Review - Exercises - Page 1189: 11


$F$ is conservative with potential function $$f(x,y)=xe^{xy}+e^y+C$$

Work Step by Step

$F(x,y)=(1+xy)e^{xy}i+(e^y+x^2e^{xy})j$ $F(x,y)=(Pi+Qj)$ will be conservative when $P_y=Q_x$ Thus, $P_y=(2+xy)xe^{xy}$ and $Q_x=(2+xy)xe^{xy}$ Hence, the given vector field $F$ is conservative with potential function $$f(x,y)=xe^{xy}+e^y+C$$
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