# How do you find the average value of the function for f(x)=x^3, 0<=x<=2?

$2$
$\frac{1}{\textcolor{b l u e}{2} - \textcolor{b l u e}{0}} {\int}_{\textcolor{b l u e}{0}}^{\textcolor{b l u e}{2}} \setminus {x}^{3} \setminus \mathrm{dx} = \frac{1}{2} {\left[\frac{1}{4} {x}^{4}\right]}_{\textcolor{b l u e}{0}}^{\textcolor{b l u e}{2}} = \frac{1}{8} \left({\left(\textcolor{b l u e}{2}\right)}^{4} - {\left(\textcolor{b l u e}{0}\right)}^{4}\right) = \frac{1}{8} \left(16 - 0\right) = 2$