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 $${let}\:{u}_{{k}} =\:\int_{−\frac{\pi}{\mathrm{2}}\:+{k}\pi} ^{−\frac{\pi}{\mathrm{2}}\:+\left({k}+\mathrm{1}\right)\pi} \:\:{e}^{−{t}} \:{cost}\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{u}_{{k}} \\ $$$$\left.\mathrm{2}\right)\:{let}\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{u}_{{k}} \:\:\:\:\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}}…
Question Number 42795 by maxmathsup by imad last updated on 02/Sep/18 $${calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{4}} \right)^{\mathrm{2}} } \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on…
Question Number 42796 by maxmathsup by imad last updated on 02/Sep/18 $${calculate}\:{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{2}} }\:{arctan}\left({x}\right){dx} \\ $$ Commented by maxmathsup by imad last updated…
Question Number 42793 by maxmathsup by imad last updated on 02/Sep/18 $${find}\:{f}\left({a}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\left({a}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{3}} }\:\:\:{with}\:{a}>\mathrm{0} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…
Question Number 42792 by maxmathsup by imad last updated on 02/Sep/18 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\mathrm{1}+{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{3}} }{dx}\: \\ $$ Commented by behi83417@gmail.com last updated on 03/Sep/18…
Question Number 42791 by maxmathsup by imad last updated on 02/Sep/18 $${find}\:\:\int\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}\:} +\mathrm{1}\right)\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \\ $$ Answered by MJS last updated on 02/Sep/18 $$\mathrm{I}\:\mathrm{know}\:\mathrm{this}\:\mathrm{because}\:\mathrm{of}\:\mathrm{the}\:\mathrm{hyperbola}\:\mathrm{formuls} \\…
Question Number 42790 by maxmathsup by imad last updated on 02/Sep/18 $$\left.\mathrm{1}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{t}}{\mathrm{1}+{t}^{\mathrm{4}} }\:{dt} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{t}}{\mathrm{1}+{t}^{\mathrm{4}} }{dt} \\ $$$$\left.\mathrm{3}\right)\:{calculste}\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{t}}{\mathrm{1}+{t}^{\mathrm{4}} }{dt}\:…
Question Number 108325 by john santu last updated on 16/Aug/20 $$\:\:\:\frac{\multimap{JS}\multimap}{−−−−} \\ $$$$\int\:\frac{{dx}}{{x}^{\mathrm{8}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)}\:=\:? \\ $$ Commented by john santu last updated on 16/Aug/20…