# What is the average value of the function f(x) = x - (x^2)  on the interval [0,2]?

Sep 21, 2016

The average value of $f$ on $\left[a , b\right\}$ is $\frac{1}{b - a} {\int}_{a}^{b} f \left(x\right) \mathrm{dx}$.

#### Explanation:

For this function on this interval, I get $- \frac{1}{3}$

Ave$= \frac{1}{2 - 0} {\int}_{0}^{2} \left(x - {x}^{2}\right) \mathrm{dx}$

$= \frac{1}{2} {\left[{x}^{2} / 2 - {x}^{3} / 3\right]}_{0}^{2}$

$= \frac{1}{2} \left[\left(\frac{4}{2} - \frac{8}{3}\right) - \left(0\right)\right]$

$= \frac{1}{2} \left(- \frac{2}{3}\right) = - \frac{1}{3}$