Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 5: Integrals - Practice Exercises - Page 308: 70

Answer

Yes, see explanations.

Work Step by Step

Step 1. By definition, the average value of an integrable function $f(x)$ over an interval of $[a,b]$ can be written as $\bar f=av(f)=\frac{1}{b-a}\int_a^b f(x)dx$. Step 2. Given that the interval length is $2$, we have $b-a=2$ and $\bar f=av(f)=\frac{1}{2}\int_a^b f(x)dx$ which equals to half of the function's integral over the interval.
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