# How do you find the average value of x^3 as x varies between -1 and 2?

##### 1 Answer
Jan 23, 2017

$= \frac{5}{4}$

#### Explanation:

Average value of $f \left(x\right)$ over interval $\left[a , b\right]$ is $\overline{f} \left(x\right) = \frac{{\int}_{a}^{b} f \left(x\right) \mathrm{dx}}{b - a}$

Here that means that:

$\overline{f} \left(x\right) = \frac{{\int}_{- 1}^{2} {x}^{3} \mathrm{dx}}{2 - \left(- 1\right)}$

$= \frac{{\left[{x}^{4} / 4\right]}_{- 1}^{2}}{3} = \frac{5}{4}$