How should I calculate the Lebesgue integral of logarithm function

Averie Ray

Averie Ray

Answered question

2022-04-23

How should I calculate the Lebesgue integral of logarithm function from zero to infinity?
Does the area under the ln(x) in (0,+) is measurable? If yes, how can I calculate it?

Answer & Explanation

wellnesshaus4n4

wellnesshaus4n4

Beginner2022-04-24Added 24 answers

The area between 0 and 1 is the negative of 0exdx which is finite. On the other hand, the area between 1 and s infinite (for example logx is larger than the indicator function of (e,)
Brennen Davies

Brennen Davies

Beginner2022-04-25Added 25 answers

0logx,dx=limb,,ϵ0ϵblogxdx=limb,,ϵ0(xlogxx)ϵb=
=limb,ϵ0[(blogbb)(ϵlogϵϵ)]=

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?