Calculus (3rd Edition)

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 - Preliminary Questions - Page 846: 6


(b) and (c).

Work Step by Step

We know that for any odd function $f(x)$, the integral $\int_{-a}^af(x)dx=0$. Now, since $xy^2$ and $\sin x$ are odd functions in $x$ and $x$ changes from $-1$ to $1$, then the integrals that will be zero are (b) and (c). The function in (d) is not odd and the function in (a) is not odd over $x$.
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