Determine the convergence of the integral I=∫01xα−1(1−x)β−1 dxI = \int_0^1 x^{\alpha-1} (1-x)^{\beta-1} \, dxI=∫01xα−1(1−x)β−1dx for α,β∈R\alpha, \beta \in \mathbb{R}α,β∈R.
Converges if and only if α>0\alpha > 0α>0 and β>0\beta > 0β>0
Converges for all α,β>1\alpha, \beta > 1α,β>1
Converges if α+β>1\alpha + \beta > 1α+β>1
Always diverges for α<1\alpha < 1α<1