Prove that:

1-x)^{n-1}dx = \frac{n!\:m!}{(m+n)!}" alt="n\:\int_{0}^{1} x^m \1-x)^{n-1}dx = \frac{n!\:m!}{(m+n)!}" />

Is this correct?

L.H.S

= n.B(m, n -1) , where B(x, y) is Beta function

= n. m!(n-1)!/((m + n - 1 + 1)!)

= n(n-1)!m!/((m+n)!)

= R.H.S