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} \\ $$ Terms…
Question Number 42798 by maxmathsup by imad last updated on 02/Sep/18 $${find}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} \sqrt{\mathrm{1}−{x}^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup by imad last…
Question Number 42799 by maxmathsup by imad last updated on 02/Sep/18 $${let}\:{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{8}}} \:\:{e}^{−\mathrm{2}{t}} \:{cos}^{\mathrm{4}} {t}\:\:\:\:{and}\:{J}\:\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{8}}} \:{e}^{−\mathrm{2}{t}} \:{sin}^{\mathrm{4}} {dt} \\ $$$${find}\:{the}\:{values}\:{of}\:{I}\:{andJ}\:. \\ $$ Commented…
Question Number 42797 by maxmathsup by imad last updated on 02/Sep/18 $${let}\:{u}_{{k}} =\:\int_{−\frac{\pi}{\mathrm{2}}\:+{k}\pi} ^{−\frac{\pi}{\mathrm{2}}\:+\left({k}+\mathrm{1}\right)\pi} \:\:{e}^{−{t}} \:{cost}\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{u}_{{k}} \\ $$$$\left.\mathrm{2}\right)\:{let}\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{u}_{{k}} \:\:\:\:\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}}…