Menu Close

Category: Integration

Find-the-value-of-the-following-expression-Im-Li-2-2-0-pi-2-ln-sin-x-dx-

Question Number 213776 by mnjuly1970 last updated on 16/Nov/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{F}{ind}\:\:{the}\:\:{value}\:{of}\:\:{the}\:{following} \\ $$$$\:\:\:\:\:\:\:\:\:\:{expression}. \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\Omega=\:\:\:\frac{\:\mathrm{I}{m}\left(\:\mathrm{Li}_{\mathrm{2}} \:\left(\mathrm{2}\right)\right)}{\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\mathrm{ln}\left(\mathrm{sin}\left({x}\:\right)\right)\:{dx}}\:\:=\:? \\ $$ Answered by…

Question-213656

Question Number 213656 by efronzo1 last updated on 12/Nov/24 Answered by golsendro last updated on 13/Nov/24 $$\:\:\left(\mathrm{i}\right)\:\mathrm{g}\left(\mathrm{4}−\mathrm{x}\right)=\:−\mathrm{g}\left(\mathrm{x}\right)\: \\ $$$$\:\:\:\:\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:\mathrm{g}\left(\mathrm{x}\right)\mathrm{dx}\:=\:\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:\mathrm{g}\left(\mathrm{4}−\mathrm{x}\right)\mathrm{dx}\: \\ $$$$\:\:\:\:\:\:\:\:\underset{\mathrm{0}}…