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Real Analysis : Integrable Functions

Let f:[0,1]-->R be a Riemann integrable function. Prove that
lim n-->∞ ∫ (from 0 to 1) x^n f(x)dx = 0.

I do not know where to begin on this problem. It seems like it should be easy though.

Solution Preview

It is evident that x comes from [0, 1]. So lim n-->∞(x^n)=0
Give that f is Riemann Integrable function. Hence f must be bounded. Let the bounds of f are m and M. We should then have ...

Solution Summary

An integrable functions proof is provided.

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