# Improper integral

1. Feb 9, 2008

### covariance64

1. The problem statement, all variables and given/known data

Show that the integral of (1/x)sin(1/x)dx from 0 to 1 is converges absolutely?

2. Relevant equations

3. The attempt at a solution

Should we use the comparison test in this situation?

2. Feb 9, 2008

### quasar987

Try a change of variables first.

3. Jun 15, 2011

### elabed haidar

change of variable u=1/x you will get from 1 to infinite integral of -sinu over u after that you do integration by parts and you will get your answer sinu / u is always convergent