Let-f-C-0-1-0-1-Prove-that-lim-n-0-1-n-f-1-n-i-1-n-x-i-dx-1-dx-n-f-1-2-

Question Number 75079 by ~blr237~ last updated on 07/Dec/19

Let f \in C ([0, 1], [0, 1])

Prove that \lim_{n \to \infty} \int_{{[0, 1]}^{n}} f (\frac{1}{n} \underset{i = 1}{\sum^{n}} x_{i}) {dx}_{1} \dots . {dx}_{n} = f (\frac{1}{2})