## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 16 - Multiple Integration - 16.1 Integration in Two Variables - Exercises - Page 846: 17

#### Answer

$0$

#### Work Step by Step

We know that sine is an odd function and $\sin (-x)=-\sin x$ Because of symmetry, the (negative) signed volume of the region below the $xy$-plane where $\pi \leq x \leq 2\pi$ cancels with the (positive) signed volume of the region above the xy-plane where $0 \leq x \leq \pi$. Thus, the result is $0$.

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