Thank you Opalg for your answer.
In fact I have already proved that:
$$\displaystyle \lim_{n\to+\infty} n\int_{0}^1 x^ng(x)\mathrm{d}x=g(1)$$
with $$g \in\mathcal{C}^0(\left[0,1\right],\mathbb{R})$$.My problem is to prove this:
$$\displaystyle \int_0^1 x^n...
Hello everybody,
I have proved that:
$$\displaystyle \lim_{n\to+\infty} n\int_{0}^1 x^ng(x)\mathrm{d}x=g(1)$$
with $$g \in\mathcal{C}^0(\left[0,1\right],\mathbb{R})$$.But I don't know how to prove this:
$$\displaystyle \int_0^1 x^n...