Category: Integration

Question Number 29972 by abdo imad last updated on 14/Feb/18 $${let}\:{give}\:\mid{x}\mid<\mathrm{1}\:{find}\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{d}\theta}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} {cos}^{\mathrm{2}} \theta}}\:. \\ $$ Commented by abdo imad last updated on 18/Feb/18…

Question Number 29957 by 7980812906 last updated on 14/Feb/18 $$\int\mathrm{3}{x}\mathrm{d}{x} \\ $$ Answered by Joel578 last updated on 14/Feb/18 $$\int\:\mathrm{3}{x}\:{dx}\:=\:\frac{\mathrm{3}}{\mathrm{2}}{x}^{\mathrm{2}} \:+\:{C} \\ $$ Terms of…

Question Number 95449 by bobhans last updated on 25/May/20 $$\int\int\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\:\mathrm{dxdy}\:=\: \\ $$$$\mathrm{where}\:\mathrm{D}\::\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:\leqslant\:\mathrm{100}\: \\ $$ Commented by mr W last updated on…

Question Number 160979 by amin96 last updated on 10/Dec/21 $$\Omega=\int_{\mathrm{0}} ^{\mathrm{1}} \boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{n}}−\mathrm{1}} \boldsymbol{\mathrm{ln}}\left(\mathrm{1}−\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{dx}}=???\:\:\: \\ $$$$\boldsymbol{\mathrm{n}}\geqslant\mathrm{1} \\ $$ Answered by qaz last updated on 10/Dec/21 $$\Omega=−\underset{\mathrm{k}=\mathrm{1}}…

Question Number 160928 by mnjuly1970 last updated on 09/Dec/21 $$ \\ $$$$\:\:\:\:\:\:\:{calculate} \\ $$$$ \\ $$$$\:\:\:\:\Omega\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\zeta\:\left(\:\mathrm{1}+\:{n}\:\right)\:−\mathrm{1}}{{n}\:+\:\mathrm{1}}\:\overset{?} {=}\:\mathrm{1}−\:\gamma\: \\ $$$$\:−−−−−−−−−−− \\ $$ Answered by…