Menu Close

let-consider-two-real-numbers-p-and-such-as-p-2-q-2-pq-Prove-that-J-0-dv-q-1-q-v-p-p-1-

Tinku Tara
Pin




Question Number 65825 by ~ À ® @ 237 ~ last updated on 04/Aug/19
let consider two real numbers p and such as p^2 −q^2 =pq Prove that J= ∫_0 ^∞ (dv/(^q (√((1+^q (√(v^p )) )^p ))))= 1
$${let}\:{consider}\:\:{two}\:{real}\:{numbers}\:{p}\:{and}\:{such}\:{as}\:{p}^{\mathrm{2}} −{q}^{\mathrm{2}} ={pq} \\ $$$${Prove}\:{that} \\ $$$$\:\:\:{J}=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dv}}{\:^{{q}} \sqrt{\left(\mathrm{1}+\:^{{q}} \sqrt{{v}^{{p}} \:}\:\right)^{{p}} }}=\:\mathrm{1} \\ $$$$ \\ $$

Pin