(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Ifaandbare positive numbers, show that [tex]\int_0^1 x^a*(1-x)^b\,dx = \int_0^1 x^b*(1-x)^a\,dx[/tex] usingonlyU 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.

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# Homework Help: Prove two integrals are the same using U substitution

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