# How do you find the average value of #f(x)=x^5-4x^3+2x-1# as x varies between #[-2,2]#?

##### 2 Answers

#### Explanation:

The average value of a function is found using the following equation:

#f_(ave)=1/(b-a)*int_a^bf(x)dx#

on some interval

Therefore:

#f_(ave)=1/4int_(-2)^2(x^5-4x^3+2x-1)dx#

This is a basic integral.

#=>f_(a v e)=1/4(1/6x^6-x^4+x^2-x)]_(-2)^2#

#=1/4*-4#

#=-1#

Morgan has given a fine answer. I want to mention a fact that can simplify the integration needed for this question.

#### Explanation:

A function

If

In this question the first four terms of the polynomial form an odd function that is integrable on any closed interval, so

# = {: -x]_-2^2 = -(2)-(-(-2)) = -4#