Question Number 34720 by abdo mathsup 649 cc last updated on 10/May/18
$${let}\:{B}\left({p},{q}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{p}−\mathrm{1}} \left(\mathrm{1}−{x}\right)^{{q}−\mathrm{1}} {dx} \\ $$$${calculate}\:{B}\left(\frac{\mathrm{1}}{\mathrm{3}},\:\frac{\mathrm{1}}{\mathrm{3}}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{B}\left(\frac{\mathrm{1}}{\mathrm{2}}\:,\frac{\mathrm{2}}{\mathrm{3}}\right)\:. \\ $$