展开全部
∫(上限1,下限0) x^m *(1-x)^n dx
= 令t=x-(1/2), ∫(上限1/2,下限-1/2) ((1/2)+t)^m *((1/2)-t)^n dt
所以:
∫(上限1,下限0) x^n *(1-x)^m dx
= 令t=x-(1/2), ∫(上限1/2,下限-1/2) ((1/2)+t)^n *((1/2)-t)^m dt
= -∫(上限-1/2,下限1/2) ((1/2)-t)^n *((1/2)+t)^m dt
= ∫(上限1/2,下限-1/2) ((1/2)+t)^m *((1/2)-t)^n dt
=∫(上限1,下限0) x^m *(1-x)^n dx
= 令t=x-(1/2), ∫(上限1/2,下限-1/2) ((1/2)+t)^m *((1/2)-t)^n dt
所以:
∫(上限1,下限0) x^n *(1-x)^m dx
= 令t=x-(1/2), ∫(上限1/2,下限-1/2) ((1/2)+t)^n *((1/2)-t)^m dt
= -∫(上限-1/2,下限1/2) ((1/2)-t)^n *((1/2)+t)^m dt
= ∫(上限1/2,下限-1/2) ((1/2)+t)^m *((1/2)-t)^n dt
=∫(上限1,下限0) x^m *(1-x)^n dx
推荐律师服务:
若未解决您的问题,请您详细描述您的问题,通过百度律临进行免费专业咨询