Posted by haifeng on 2014-11-28 19:18:52 last update 2023-08-23 09:11:26 | Answers (1) | 收藏
设 $f\in C^2[0,1]$, 满足 $f(1)=0$, $f'(1)=a$. 证明
\[ \lim_{n\rightarrow\infty}n^2\int_0^1 x^n f(x)\mathrm{d}x=-a. \]
