# What is the average value of the function f ( x ) = x &#x2212;<!-- − --> ( x

What is the average value of the function $f\left(x\right)=x-\left({x}^{2}\right)$ on the interval [0,2]?
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Pranav Greer
For this function on this interval, I get $-\frac{1}{3}$
Ave $=\frac{1}{2-0}{\int }_{0}^{2}\left(x-{x}^{2}\right)dx$
$=\frac{1}{2}\left[\frac{{x}^{2}}{2}-\frac{{x}^{3}}{3}{\right]}_{0}^{2}$
$=\frac{1}{2}\left[\left(\frac{4}{2}-\frac{8}{3}\right)-\left(0\right)\right]$
$=\frac{1}{2}\left(-\frac{2}{3}\right)=-\frac{1}{3}$