How do you determine if the improper integral converges or diverges #int xe^-x dx # from 0 to infinity?
1 Answer
Explanation:
First let is find
The formula for integration by parts is:
Essentially we would like to find one function that simplifies when differentiated, and one that simplifies when integrated (or is at least integrable).
In this case differentiating x simplifies whereas
Let
So IBP gives:
This next part is not a vigorous proof, but it is adequate (unless you are studying for a Maths degree!)
And, so we have:
Now
Hence,