Question Number 36752 by prof Abdo imad last updated on 05/Jun/18 $${find}\:\:\int\:\:\:\frac{{dx}}{{arcsinx}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:. \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 05/Jun/18 $${is}\:{it}\:\int\frac{{dx}}{{sin}^{−\mathrm{1}} \left({x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:\right)}\:\:{pls}\:{clarify}…
Question Number 36753 by prof Abdo imad last updated on 05/Jun/18 $${find}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:{x}^{{n}} \:{arctan}\left({x}\right){dx}\:. \\ $$ Commented by prof Abdo imad last updated…
Question Number 167823 by cortano1 last updated on 26/Mar/22 Commented by dangduomg last updated on 26/Mar/22 $$\mathrm{actually}\:\mathrm{very}\:\mathrm{long}\:\mathrm{answer} \\ $$ Commented by MJS_new last updated on…
Question Number 36747 by prof Abdo imad last updated on 05/Jun/18 $${let}\:{f}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{{sin}\left({nx}\right)}{{n}}\:{x}^{{n}} \\ $$$$\left.\mathrm{1}\left.\right)\:{prove}\:{that}\:{f}\:{is}\:{C}^{\mathrm{1}} \:{on}\:\right]−\mathrm{1},\mathrm{1}\left[\right. \\ $$$$\left.\mathrm{2}\right){calculate}\:{f}^{'} \left({x}\right)\:{and}\:{prove}\:{that} \\ $$$${f}\left({x}\right)={arctan}\left(\:\frac{{xsinx}}{\mathrm{1}−{x}\:{cosx}}\right) \\ $$ Commented…
Question Number 102275 by malwaan last updated on 07/Jul/20 $$\int_{\mathrm{1}} ^{\mathrm{2}} \:\boldsymbol{{ln}}\left(\frac{\boldsymbol{{x}}^{\mathrm{4}} \:+\:\mathrm{4}}{\boldsymbol{{x}}^{\mathrm{2}} \:+\:\mathrm{4}}\right)\frac{\boldsymbol{{dx}}}{\boldsymbol{{x}}} \\ $$ Commented by Dwaipayan Shikari last updated on 08/Jul/20 $$\mathrm{0}…
Question Number 36737 by abdo mathsup 649 cc last updated on 04/Jun/18 $${let}\:{g}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\:\mathrm{1}−{e}^{{i}\theta} {x}^{\mathrm{2}} \right){dx} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{g}\left(\theta\right)\:.\theta\:{from}\:{R}. \\ $$ Commented by math khazana…
Question Number 36738 by MJS last updated on 04/Jun/18 $$\left(\mathrm{1}\right)\:\:\:\:\:\int\frac{{d}\alpha}{\left(\mathrm{1}+\mathrm{sin}\:\mathrm{2}\alpha\right)^{\mathrm{2}} }= \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\int\frac{{d}\beta}{\left(\mathrm{1}+\mathrm{cos}\:\mathrm{2}\beta\right)^{\mathrm{2}} }= \\ $$$$\left(\mathrm{3}\right)\:\:\:\:\:\int\frac{{d}\gamma}{\left(\mathrm{1}+\mathrm{sin}\:\mathrm{2}\gamma\right)\left(\mathrm{1}+\mathrm{cos}\:\mathrm{2}\gamma\right)}= \\ $$ Commented by behi83417@gmail.com last updated on 05/Jun/18…
Question Number 36736 by abdo mathsup 649 cc last updated on 04/Jun/18 $${let}\:\:{f}\left(\theta\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left(\mathrm{1}−{e}^{{i}\theta} {x}\right){dx} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left(\theta\right) \\ $$ Commented by prof Abdo imad…
Question Number 36728 by a1bgt3@gmail.com last updated on 04/Jun/18 $${the}\:{improper}\:{integral}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:{converges}\:{to} \\ $$ Commented by abdo.msup.com last updated on 05/Jun/18 $${I}\:={lim}_{\xi\rightarrow\mathrm{0}} \:\int_{\xi} ^{\mathrm{1}}…
Question Number 102233 by nimnim last updated on 07/Jul/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{under}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{y}=\sqrt{\mathrm{a}^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} } \\ $$$$\mathrm{included}\:\mathrm{between}\:\mathrm{the}\:\mathrm{lines}\:\mathrm{x}=\mathrm{0}\:\mathrm{and}\:\mathrm{x}=\mathrm{4} \\ $$$$ \\ $$$$\mathrm{plz}\:\mathrm{help}….. \\ $$ Answered by 30-04-1945 last updated…