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

##### 1 Answer

Nov 23, 2016

#### Explanation:

The average value of the function

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

With the given information this translates into

#1/(5-1)int_1^5cos(x)dx#

The antiderivative of

#=1/4[sin(x)]_1^5=1/4(sin(5)-sin(1))#

This is as simplified as we can get without using a calculator.

#1/4(sin(5)-sin(1))approx-0.45010#