定积分(0→π/2)xsinxdx
问题描述:
定积分(0→π/2)xsinxdx
答
用分部积分法做
∫ xsinx dx (u = x,v' = sinx,v = -cosx)
= -xcosx - ∫ -cosx dx
= -xcosx + sinx + C
定积分从0到π/2
= (0 + 1) - (0)
= 1