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

##### 1 Answer

Nov 25, 2016

#### Explanation:

The average value of the function

#1/(b-a)int_a^bf(x)dx#

Which here gives us the average value

#1/(1-0)int_0^1(-x^5+3x^3)dx#

Integrating term by term using

#=[-x^6/6+(3x^4)/4]_0^1#

The

#-1/6+3/4=7/12#