# How do you find the average value of the function for f(x)=1-x^4, -1<=x<=1?

Aug 30, 2017

The average value is $\frac{4}{5}$.

#### Explanation:

The average value is given by

$A = \frac{1}{b - a} {\int}_{a}^{b} f \left(x\right) \mathrm{dx}$

Where $f \left(x\right)$ is a continuous function on $\left[a , b\right]$.

$A = \frac{1}{1 - \left(- 1\right)} \int 1 - {x}^{4}$

$A = \frac{1}{2} {\left[\left(x - \frac{1}{5} {x}^{5}\right)\right]}_{-} {1}^{1}$

$A = \frac{1}{2} \left(1 - \frac{1}{5} - \left(- 1 - \frac{1}{5} {\left(- 1\right)}^{5}\right)\right)$

$A = \frac{1}{2} \left(\frac{4}{5} + 1 - \frac{1}{5}\right)$

$A = \frac{1}{2} \left(\frac{8}{5}\right)$

$A = \frac{4}{5}$

Hopefully this helps!