# How do you find the average value of the function for #f(x)=x/(x+1), 0<=x<=4#?

##### 1 Answer

#### Explanation:

The average value of a function

So here, we wish to find:

#1/(4-0)int_0^4x/(x+1)dx#

There are a lot of ways to solve this integral. I would try the substitution

We also should realize that

#=1/4int_1^5(u-1)/udu#

Split up this integral:

#=1/4int_1^5(1-1/u)du#

Both of these are common integrals:

#=1/4[(u-lnabsu)]_(u=1)^(u=5)#

Evaluating:

#=1/4[(5-lnabs5)-(1-lnabs(1))#

Note that

#=1/4(4-ln5)#

#=1-1/4ln5#

#approx2.39056#