# How do you find the average value of f(x)=x^5-2x^3-2 as x varies between [-1,1]?

Evaluate $\frac{1}{1 - \left(- 1\right)} {\int}_{-} {1}^{1} \left({x}^{5} - 2 {x}^{3} - 2\right) \mathrm{dx}$
$\frac{1}{1 - \left(- 1\right)} {\int}_{-} {1}^{1} \left({x}^{5} - 2 {x}^{3} - 2\right) \mathrm{dx} = \frac{1}{2} {\int}_{-} {1}^{1} \left(- 2\right) \mathrm{dx}$
(The first two terms form an odd function whose integral from $- 1$ to $1$ is $0$.)
$= \frac{1}{2} \left(- 4\right) = - 2$