# Math Help - improper integral

1. ## improper integral

The question:
Determine if integral converges or diverges. If converges, evaluate.
int (xlnx)dx on from 0 to 1.

It isn't continuous on 0 or 1, right? ln(1)=0. How do I evaluate it when it is not continuous on both sides? Can I just choose 0 or 1 and set it up as a limit and set "b" equal to the other?

2. Originally Posted by jlmills5
The question:
Determine if integral converges or diverges. If converges, evaluate.
int (xlnx)dx on from 0 to 1.

It isn't continuous on 0 or 1, right? ln(1)=0. How do I evaluate it when it is not continuous on both sides? Can I just choose 0 or 1 and set it up as a limit and set "b" equal to the other?
It's continuous on (0, 1] (try graphing it). You need to evaluate $\lim_{b\to 0}\int_b^1 x\ln (x) \mathrm dx$.