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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.

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    See [here](http://math.stackexchange.com/questions/175413/how-can-i-prove-lim-n-to-infty-int-0-pi-2-fx-sin-2n1-x-dx-0?rq=1).2012-12-15
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    Also, [here](http://math.stackexchange.com/questions/150645/question-on-weak-convergence-example). If I kept searching, I'm sure I could find others...2012-12-15
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    This follows from the [Riemann–Lebesgue](http://en.wikipedia.org/wiki/Riemann–Lebesgue_lemma) lemma.2012-12-15

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