νεκκοιανδ

摘要： 求：\(\int \sin^{n}dx\) \[ \begin{aligned} I_n =&\int \sin^ndx \\ =&-\int \sin^{n-1}d\cos x \\ =&-\sin^{n-1}x\cos x+\int \cos x(n-1)\sin^{n-2}\cos xdx \ 阅读全文

摘要： 设 \(f(x) \in C^{1}[a,b]\)，且 \(f(a)=0\) 求证：\(\int_{a}^{b}f^2(x)dx \le \frac{(b-a)^2}{2}\int_a^b[f'(x)]^2dx\) \[ \begin{aligned} &\because f(x)=f(x)-f(a 阅读全文