Question

问题

Questions in category: 定积分 (Definite Integral).

求 $I_{n} = \int_{0}^{\frac{π}{2}} \sin^{n} x d x$ 与 $I_{n} = \int_{0}^{\frac{π}{2}} \cos^{n} x d x$

Posted by haifeng on 2011-05-22 20:03:20 last update 2014-12-29 11:43:11 | Answers (1) | 收藏

$I_{n} = {\begin{cases} \frac{(2 k - 1)!!}{(2 k)!!} \cdot \frac{π}{2}, & if n = 2 k; \\ \frac{(2 k)!!}{(2 k + 1)!!}, & if n = 2 k + 1. \end{cases}$

类似的, 求

$I_{n} = \int_{0}^{π} x \cos^{n} x d x, I_{n} = \int_{0}^{π} x \sin^{n} x d x .$