Question Number 42823 by rahul 19 last updated on 03/Sep/18 $$\mathrm{Evaluate}\:: \\ $$$$\int_{−\mathrm{5}} ^{\:\mathrm{5}} \:{x}^{\mathrm{2}} \left[{x}+\frac{\mathrm{1}}{\mathrm{2}}\right]{dx}\:=\:\:? \\ $$$${where}\:\left[.\right]=\:{greatest}\:{integer}\:{function} \\ $$ Commented by prof Abdo imad…
Question Number 42812 by maxmathsup by imad last updated on 02/Sep/18 $${study}\:{the}\:{convervence}\:{of}\:\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{arctan}\left({x}−\mathrm{1}\right)}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} }\:{dx} \\ $$ Commented by maxmathsup by imad last updated…
Question Number 42810 by maxmathsup by imad last updated on 02/Sep/18 $${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{x}^{\mathrm{5}} }{\mathrm{1}+{x}^{\mathrm{7}} }{dx}\:\:. \\ $$ Commented by prof Abdo imad last updated…
Question Number 42809 by maxmathsup by imad last updated on 02/Sep/18 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{tdt}}{\left(\mathrm{1}+{t}^{\mathrm{4}} \right)^{\mathrm{2}} } \\ $$ Commented by prof Abdo imad last updated…
Question Number 42806 by maxmathsup by imad last updated on 02/Sep/18 $${let}\:\:{u}_{{n}} =\:\int_{{n}} ^{{n}+\mathrm{2}} \:\:\:\frac{\left({t}+{n}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} }{{t}^{\frac{\mathrm{1}}{\mathrm{3}}} }{dt} \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} \:{u}_{{n}} \\ $$ Terms of Service…
Question Number 42804 by maxmathsup by imad last updated on 02/Sep/18 $${calculate}\:\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\:\:\:\:\frac{{dx}}{\:\sqrt{\mathrm{4}{x}^{\mathrm{2}} \:−\mathrm{1}}\:+\sqrt{\mathrm{4}{x}^{\mathrm{2}} \:+\mathrm{1}}} \\ $$ Commented by maxmathsup by imad last updated…
Question Number 42803 by maxmathsup by imad last updated on 02/Sep/18 $${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}{dx}\: \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 03/Sep/18 $$\int_{\mathrm{0}}…
Question Number 42801 by maxmathsup by imad last updated on 02/Sep/18 $${find}\:{f}\left({x}\right)\:=\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\:\:\:\frac{{cosxdx}}{\mathrm{2}{cos}^{\mathrm{2}} {x}\:+{sin}^{\mathrm{2}} {x}\:+\mathrm{1}} \\ $$ Commented by maxmathsup by imad last updated…
Question Number 42802 by maxmathsup by imad last updated on 02/Sep/18 $${calculate}\:\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\frac{\mathrm{5}}{\mathrm{4}}} \:\:\:\frac{{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{2}+{x}−{x}^{\mathrm{2}} }}{dx} \\ $$ Commented by maxmathsup by imad last updated…
Question Number 42800 by maxmathsup by imad last updated on 02/Sep/18 $${find}\:\int\:\:\:\:\:\frac{{sinx}}{\mathrm{1}+\mathrm{2}\:{cosx}}{dx} \\ $$ Answered by malwaan last updated on 03/Sep/18 $$−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\mid\mathrm{1}+\mathrm{2cosx}\mid+\mathrm{c} \\ $$ Terms…