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.
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 ...
An integrable functions proof is provided.