Calculus 8th Edition

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

Chapter 6 - Inverse Functions - Review - Exercises - Page 507: 111

Answer

$\frac{2\ln2}{3}$

Work Step by Step

The average value of $f$ over $[1,4]$ is: $$\frac{1}{4-1}\int_{1}^{4}\frac{1}{x}dx$$ $$\frac{1}{3}\int_{1}^{4}\frac{1}{x}dx$$ $$\frac{1}{3}[\ln x]_{1}^{4}=\frac{1}{3}(\ln 4-\ln 1)=\frac{\ln4}{3}=\frac{2\ln2}{3}$$
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