Menu Close

Category: Integration

Advanced-Calculus-evaluation-the-value-of-0-pi-2-sin-2-x-ln-sin-x-dx-solution-a-0

Question Number 140588 by mnjuly1970 last updated on 09/May/21 $$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…….{Advanced}\:….\bigstar\bigstar\bigstar….{Calculus}……. \\ $$$$\:\:\:\:\:\:\:\:{evaluation}\:{the}\:{value}\:{of}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}\::=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {sin}^{\mathrm{2}} \left({x}\right).{ln}\left({sin}\left({x}\right)\right){dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:{solution}:: \\ $$$$\:\:\:\:\:\:\:\xi\:\left({a}\right):=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {sin}^{\mathrm{2}+{a}}…