Possible Duplicate:
How can I prove $\lim_{n \to \infty} \int_{0}^{\pi/2} f(x) \sin ((2n+1) x) dx =0 $?
I have trouble evaluating the following limit? $ \lim_{n\to\infty}\int_{0}^{2\pi}\sin(nx)f(x)dx $ for any square integrable function $f(x)$.
I would very much appreciate your help.