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