Question

Show that ∫(x - a)^{m -1} (b - x)^{n - 1}dx for x ∈ [a, b] = (b - a)^{m + n - 1} β(m, n).

Answer 1

Substitute x – a = (b – a)t

so that dx = (b – a)dt

when x = a, t = 0 and

when x = b, t = 1