证明: ∫(上π下0)sin^nxdz=2∫(上π/2下0)sin^nxdx
问题描述：
证明: ∫(上π下0)sin^nxdz=2∫(上π/2下0)sin^nxdx
如题,详细过程的最好,不胜感激QWQ
答
令t=π-x∫(π/2->π) (sinx)^ndx =∫(π/2->0) (sin(π-t))^nd(-t)=∫(0->π/2) (sint)^ndt=∫(0->π/2) (sinx)^ndx所以∫(0->π) (sinx)^ndx=∫(0->π/2) (sinx)^ndx+∫(π/2->π) (sinx)^ndx =2∫(0->π/2) (sinx...