Question Number 89343 by Ar Brandon last updated on 17/Apr/20
$${Given}\:\alpha\:{and}\:\beta\:\in\mathbb{N}\:{such}\:{that} \\ $$$${I}\left(\alpha,\beta\right)=\int_{} ^{\mathrm{1}} {t}^{\alpha} \left(\mathrm{1}−{t}\right)^{\beta} {dt} \\ $$$${show}\:{that} \\ $$$${I}\left(\alpha;\beta\right)=\frac{\alpha!\beta!}{\left(\alpha+\beta+\mathrm{1}\right)!} \\ $$
Commented by abdomathmax last updated on 17/Apr/20
$${sir}\:{brandon}\:{this}\:{question}\:{is}\:{solved}\:{take}\:{a}\:{look} \\ $$$${at}\:{the}\:{platform}... \\ $$
Commented by Ar Brandon last updated on 17/Apr/20
$${I}\:{got}\:{it}\:{thanks} \\ $$