## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 16 - Multiple Integration - 16.1 Integration in Two Variables - Exercises - Page 846: 24

#### 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}

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