1. The problem statement, all variables and given/known data If a and b are positive numbers, show that [tex]\int_0^1 x^a*(1-x)^b\,dx = \int_0^1 x^b*(1-x)^a\,dx[/tex] using only U substitution. 2. Relevant equations Just U substitution and the given equation--I can't use multiplication rules or anything like that; otherwise it would be easy. 3. The attempt at a solution I tried to set U=(1-x) and I end up with [tex]\int_0^1 (1-U)^a*(U)^B\,dx[/tex] for the right side, but that doesn't seem to get me anywhere. I know I somehow need to switch the places of the x and (1-x) but I can't seem to get around going in a circle and ending up with what I started with.