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Category: Integration

nice-calculus-prove-n-1-2n-1-1-n-1-log-2-

Question Number 138065 by mnjuly1970 last updated on 09/Apr/21 $$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:…{nice}\:…\:…\:…\:{calculus}… \\ $$$$\:\:\:\:\:\:\:{prove}:: \\ $$$$\:\:\:\:\:\:\:\:\:\Omega=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\zeta\left(\mathrm{2}{n}+\mathrm{1}\right)−\mathrm{1}}{{n}+\mathrm{1}}\:=−\gamma+{log}\left(\mathrm{2}\right) \\ $$ Answered by Ñï= last updated…

advanced-calculus-prove-that-0-1-x-sin-2pix-dx-pi-2-

Question Number 138041 by mnjuly1970 last updated on 09/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:…….{advanced}\:…\:…\:…\:{calculus}…… \\ $$$$\:\:{prove}\:\:{that}\:::: \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \psi\left({x}\right).{sin}\left(\mathrm{2}\pi{x}\right){dx}=−\frac{\pi}{\mathrm{2}}\:…\checkmark \\ $$$$ \\ $$ Answered by Dwaipayan Shikari last…

0-pi-sin-3x-cos-x-dx-

Question Number 6979 by Fitrah A last updated on 04/Aug/16 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}\left({sin}\:\mathrm{3}{x}\:+\:{cos}\:{x}\right)\:{dx}\:=\:? \\ $$ Answered by sandy_suhendra last updated on 04/Aug/16 $$=\left[−\frac{\mathrm{1}}{\mathrm{3}}{cos}\:\mathrm{3}{x}\:+\:{sin}\:{x}\right]_{\mathrm{0}} ^{\pi} \\…