Need help with (simple) math problem (convergence of infinit integra).

[Ratamahatta]

Hello, I need help with this problem. I don't want solution (not yet anyway [img]/images/graemlins/smile.gif[/img] ), I just want some one to give me a hint.

I need to show that this integral:

int_(from 0 to a) 1/[sin(sqrt(x))] dx 0 < a < pi.

is convergent.

I know that I need to put some constant (h) in stead of 0 and then find lim_h \to 0, but I can't solve this integral. I tried substitution, but it gets very messy. I even tried writing Riemann-sum for that function and rewriting 1/sin(sqrt(x)) as a series but I had to stop because it got to complicated.

So, does anyone have any hints? Thanks!