Answer
$\frac{1}{n+1}.$
Work Step by Step
For $n\geq 0$, the average is given as follows
$$
\frac{1}{1-0} \int_{0}^{1} x^{n} d x=\int_{0}^{1} x^{n} d x=\left.\frac{1}{n+1} x^{n+1}\right|_{0} ^{1}=\frac{1}{n+1}.
$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 6 - Applications of the Integral - 6.2 Setting Up Integrals: Volume, Density, Average Value - Exercises - Page 298: 47
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