- #1

[tex]\int_0^{\frac {\pi} {2}}ln(sin(x)).dx[/tex]

My first attempt was to do the following:

[tex]\int_0^{\frac {\pi} {2}}ln(sin(x)).dx\leq\int_0^{\frac {\pi} {2}}ln(x).dx\leq\int_0^{\frac {\pi} {2}}x.dx[/tex]

But then i realized it was not an integral of positive terms, so my previous work was wrong.(This integral has all negative terms, right????)

I also realized that it is an improper integral, since [tex]ln(sin(0))[/tex] doesnt exist.

I really dont know what to do, maybe trying to express the series of ln, and sin, but i would really appreciate if you could point me into the right direction.

Thankfully Paul.