Answer
$$0$$
Work Step by Step
\begin{aligned}
\int_{-1}^{1} \int_{0}^{\pi} x^{2} \sin y d x d y &=\left.\int_{-1}^{1} \frac{1}{3}x^{3}\right|_{y=0} ^{\pi}\sin y d y\\
&= \frac{\pi^3}{3} \int_{-1}^{1} \sin y dy\\
&= 0
\end{aligned}
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 16 - Multiple Integration - 16.1 Integration in Two Variables - Exercises - Page 846: 24
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