Question Number 36936 by maxmathsup by imad last updated on 07/Jun/18 $${calculate}\:{I}_{{n}} \:=\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{dx}}{\mathrm{1}+{cos}^{\mathrm{2}} \left({nx}\right)} \\ $$ Commented by math khazana by abdo last…
Question Number 36937 by maxmathsup by imad last updated on 07/Jun/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{x}\:{dx}}{\mathrm{1}+{cosx}} \\ $$ Commented by math khazana by abdo last updated on…
Question Number 36935 by maxmathsup by imad last updated on 07/Jun/18 $${find}\:{all}\:{function}\:{f}\:{R}\rightarrow{R}\:\:{wich}\:{verify} \\ $$$$\forall\left({x},{y}\right)\in\:{R}^{\mathrm{2}} \:\:\:{f}\left({x}\right).{f}\left({y}\right)\:=\int_{{x}−{y}} ^{{x}+{y}} \:{f}\left({t}\right){dt}\:. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 102470 by M±th+et+s last updated on 09/Jul/20 $$\int\frac{{dx}}{{x}^{\mathrm{10}} +{x}^{\mathrm{2}} } \\ $$$$ \\ $$ Answered by Ar Brandon last updated on 09/Jul/20 $$\mathcal{I}=\int\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{10}}…
Question Number 36932 by maxmathsup by imad last updated on 07/Jun/18 $${let}\:{f}\:\in\:{C}^{\mathrm{0}} \left(\left[\mathrm{0},\pi\right],{R}\right)\:\:{prove}\:{that} \\ $$$${lim}_{{n}\rightarrow+\infty} \:\int_{\mathrm{0}} ^{\pi} {f}\left({x}\right)\:\mid{sin}\left({nx}\right)\mid{dx}\:=\frac{\mathrm{2}}{\pi}\:\int_{\mathrm{0}} ^{\pi} {f}\left({x}\right){dx}\:. \\ $$ Terms of Service…
Question Number 36931 by maxmathsup by imad last updated on 07/Jun/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dt}}{{x}\:−{e}^{{it}} } \\ $$ Commented by math khazana by abdo last updated…
Question Number 36930 by maxmathsup by imad last updated on 07/Jun/18 $${let}\:{u}_{{n}} =\:\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}}\:+\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{3}}\:+…..+\frac{\mathrm{1}}{\mathrm{4}{n}−\mathrm{1}} \\ $$$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:{u}_{{n}} . \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 102462 by Ar Brandon last updated on 09/Jul/20 $$\mathrm{Calculate}\:; \\ $$$$\mathrm{J}=\int\frac{\mathrm{dx}}{\mathrm{x}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\mathrm{K}=\int\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{x}−\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$$$\mathrm{L}=\int\frac{\mathrm{dx}}{\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}} \\ $$…
Question Number 167989 by cortano1 last updated on 31/Mar/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\frac{\mathrm{3}−\mathrm{cos}\:{x}}{\mathrm{3}+\mathrm{cos}\:{x}}\:{dx}\:=? \\ $$ Answered by nimnim last updated on 31/Mar/22 $$\:\:\mathrm{I}=\int\:\frac{\mathrm{6}−\mathrm{3}−\mathrm{cosx}}{\mathrm{3}+\mathrm{cosx}}\mathrm{dx}=\int\left(\frac{\mathrm{6}}{\mathrm{3}+\mathrm{cosx}}−\mathrm{1}\right)\mathrm{dx} \\ $$$$\:\:\:\:=\mathrm{6}\int\frac{\mathrm{dx}}{\mathrm{3}+\mathrm{cosx}}−\int\mathrm{dx}=\mathrm{I}_{\mathrm{1}} −\mathrm{x} \\ $$$$\:\:\:\:\mathrm{put}\:\mathrm{t}=\mathrm{tan}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\Rightarrow\:\frac{\mathrm{2}}{\mathrm{1}+\mathrm{t}^{\mathrm{2}}…
Question Number 36918 by maxmathsup by imad last updated on 07/Jun/18 $${calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\left(\mathrm{1}−{i}\right)^{−{x}^{\mathrm{2}} } {dx}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com