I need some help getting started. If $\displaystyle a$ and $\displaystyle b$ are both positive numbers how can I show that $\displaystyle \int_0^1 x^a (1-x)^b \,dx = \int_0^1 x^b (1-x)^a\,dx$
Follow Math Help Forum on Facebook and Google+
use this property $\displaystyle \int_a^b {f(x)dx} \\$ $\displaystyle a + b - x = y\\$ $\displaystyle dx = - dy\\$ $\displaystyle \int_a^b {f(x)dx} = - \int_b^a {f(a + b - y)dy = \int_a^b {f(a + b - x)dx} } \\$
That was much easier than I thought, thank you.
View Tag Cloud