Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 5 - Applications of Integration - 5.5 Average Value of a Function - 5.5 Exercises - Page 391: 13



Work Step by Step

$f$ is continuous on $[1,3]$, so by the Mean Value Theorem for Integrals there exists a number $c$ in $[1,3]$ such that $\int^3 _1 f(x) dx = f(c) (3-1), 8 = 2f(c)$; that is, there is a number $c$ such that $f(c) = \frac{8}{2} = 4$
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