# What is the average value of a function f(x)=3x^2 - 2 on the interval [0,2]?

The average value of $f$ on interval $\left[a , b\right]$ is $\frac{1}{b - a} {\int}_{a}^{b} f \left(x\right) \mathrm{dx}$
So the average value of $f \left(x\right) = 3 {x}^{2} - 2$ on the interval [(0,2] is
$\frac{1}{2 - 0} {\int}_{0}^{2} \left(3 {x}^{2} - 2\right) \mathrm{dx}$, $\text{ }$ which is $2$.