Answer
$8$
Work Step by Step
$\int\int_{D}ydA=\int_{0}^{2}\int_{y^{2}} ^{8-y^{2}} ydxdy$
$=\int_{0}^{2} [y(8-y^{2}-y^{2})]dy$
$=\int_{0}^{2} [8y-y^{3}]dy$
$=[\frac{8y^{2}}{2}-\frac{2y^{4}}{4}]_{0}^{2}$
$=16-8$
$=8$
Calculus: Early Transcendentals 8th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1285741552
ISBN 13:
978-1-28574-155-0
Chapter 15 - Review - Exercises - Page 1062: 25
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