## Calculus (3rd Edition)

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