# How do you find the average value of f(x)=x^5-2x^3+x as x varies between [-1,0]?

Feb 15, 2018

$- \frac{1}{6}$

#### Explanation:

$\text{the average value is found using}$

•color(white)(x)1/(b-a)int_a^bf(x)

$\text{where } \left[a , b\right] = \left[- 1 , 0\right]$

$\Rightarrow \frac{1}{0 - \left(- 1\right)} {\int}_{- 1}^{0} \left({x}^{5} - 2 {x}^{3} + x\right) \mathrm{dx}$

$= {\left[\frac{1}{6} {x}^{6} - \frac{1}{2} {x}^{4} + \frac{1}{2} {x}^{2}\right]}_{- 1}^{0}$

$= 0 - \left(\frac{1}{6} - \frac{1}{2} + \frac{1}{2}\right) = - \frac{1}{6}$