Question

证明∫x^m(1-x)^n dx=∫x^n(1-x)^m dx

Answer 1

令1-x=t

dx=-dt

x=0,t=1,x=1,t=0

∫[0,1]x^m(1-x)^n dx

=-∫[1,0](1-t)^mt^n dt

=∫[0,1]x^n(1-x)^m dx

定积分是正的