Ok, I just want to make sure I got it right:

I need to show if the Integral $\displaystyle \int_0^{\Pi/2} \frac {1} {sinx}$ is convergent.

So I solved the Integral: = ln[tan$\displaystyle \frac {x} {2}$]

then I put in the values $\displaystyle \Pi/2$ and $\displaystyle \alpha$ lim ->0

ln[tan$\displaystyle \frac {\Pi} {4}$] - ln[tan$\displaystyle \frac {\alpha} {2}$] =1

so the Integral is convergent and the limit is 1. Am I right? Is that the right way to do it?