Calculus (3rd Edition)

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



Work Step by Step

For $n\geq 0$, the average is given as follows $$ \frac{1}{1-0} \int_{0}^{1} x^{n} d x=\int_{0}^{1} x^{n} d x=\left.\frac{1}{n+1} x^{n+1}\right|_{0} ^{1}=\frac{1}{n+1}. $$
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