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: 20

Answer

$$2$$

Work Step by Step

Given $$f(x)=| x|, \quad[-4,4] $$ The average value is given by \begin{align*} M&=\frac{1}{b-a} \int_{a}^{b} f(x) d x\\ &=\frac{1}{4-(-4)} \int_{-4}^{4}|x| d x\\ &=\frac{1}{8} \int_{-4}^{0}-x d x+\frac{1}{8} \int_{0}^{4} x d x\\ &=-\frac{1}{8}\left[\frac{x^{2}}{2}\right]_{-4}^{0}+\frac{1}{8}\left[\frac{x^{2}}{2}\right]_{0}^{4}\\ &=2 \end{align*}
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