1. ## Integral Proof

I need some help getting started.

If $a$ and $b$ are both positive numbers

how can I show that $\int_0^1 x^a (1-x)^b \,dx = \int_0^1 x^b (1-x)^a\,dx$

2. ## Re: Integral Proof

use this property

$\int_a^b {f(x)dx} \\$

$a + b - x = y\\$

$dx = - dy\\$

$\int_a^b {f(x)dx} = - \int_b^a {f(a + b - y)dy = \int_a^b {f(a + b - x)dx} } \\$

3. ## Re: Integral Proof

That was much easier than I thought, thank you.