Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 5 - The Integral - 5.2 The Definite Integral - Exercises - Page 245: 40



Work Step by Step

Since $x$ is odd and $x^2 $ is an even function, then \begin{align*} \int_{-3}^{3}\left(9 x-4 x^{2}\right) d x&=9\int_{-3}^{3} x-4 \int_{-3}^{3}x^{2} d x\\ &=9(0)-8\int_{0}^{3}x^2dx\\ &= -8\frac{x^3}{3}\bigg|_{0}^{3}\\ &=-72 \end{align*}
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