Calculus (3rd Edition)

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

Chapter 6 - Applications of the Integral - Chapter Review Exercises - Page 319: 19



Work Step by Step

Given $$f(x)=x^{3}-2 x+2, \quad[-1,2] $$ The average value is given by \begin{align*} M&=\frac{1}{b-a} \int_{a}^{b} f(x) d x\\ &=\frac{1}{2-(-1)} \int_{-1}^{2}\left(x^{3}-2 x+2\right) d x\\ &=\left.\frac{1}{3}\left(\frac{1}{4} x^{4}-x^{2}+2 x\right)\right|_{-1} ^{2}\\ &=\frac{1}{3}\left[(4-4+4)-\left(\frac{1}{4}-1-2\right)\right]\\ &=\frac{9}{4} \end{align*}
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