Answer
$\dfrac{69}{4}$
Work Step by Step
Since, we have $\int_C xy dx +(x+y) dy$
Let us take $y^2=x \implies dy =2x dx$
Now, $\int_C xy dx +(x+y) dy=\int_C xy dx +(x+y) dy=\int_{-1}^2 2x^2+3x^3 dx$
$=\dfrac{69}{4}$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 15 - Section 15.2 - Vector Fields and Line Integrals: Work, Circulation, and Flux - Exercises - Page 838: 23
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