Calculus 8th Edition

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

Chapter 16 - Vector Calculus - Review - Exercises - Page 1189: 13


$F$ is a conservative vector field and $$\int_CF.dr=0$$

Work Step by Step

$F(x,y)=(4x^3y^2-2xy^3)i+(2x^4y-3x^2y^2+4y^3)j$ Since, $F=Pi+Qj$ will be conservative when $P_y=Q_x$ Thus, $$P_y=8x^3y-6xy^2$$ and $$Q_x=8x^3y-6xy^2$$ This shows that the given vector field $F$ is conservative. By the fundamental theorem of line integrals, we have $\int_CF.dr=f(1,1)-f(0,1)$ $=(1-1+1+k)-(0-0+1+k)$ $=0$ Hence, the result is: $\int_CF.dr=0$
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.