Question Number 37815 by prof Abdo imad last updated on 17/Jun/18 $${let}\:{I}\:\:=\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{x}} \:{cos}^{\mathrm{2}} \left(\pi\left[{x}\right]\right){dx}\:{and} \\ $$$${J}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{x}} \:{sin}^{\mathrm{2}} \left(\pi\left[{x}\right]\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}\:+{J}\:\:{and}\:{I}\:−{J} \\…
Question Number 37812 by prof Abdo imad last updated on 17/Jun/18 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\mathrm{2}{x}} {sin}\left\{\pi\left[{x}\right]\right\}{dx}\:. \\ $$ Commented by abdo mathsup 649 cc last updated…
Question Number 37813 by prof Abdo imad last updated on 17/Jun/18 $${find}\:{A}_{{n}} \:\:=\:\int_{\frac{\mathrm{1}}{{n}}} ^{\mathrm{1}} \:\:{x}\sqrt{{x}}{arctan}\left({x}+\frac{\mathrm{1}}{{x}}\right){dx} \\ $$$${then}\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} . \\ $$ Answered by tanmay.chaudhury50@gmail.com last…
Question Number 103343 by Dwaipayan Shikari last updated on 14/Jul/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{−{x}} {dx} \\ $$ Answered by mathmax by abdo last updated on 15/Jul/20…
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Question Number 168872 by MikeH last updated on 20/Apr/22 $${E}=\underset{\mathrm{0}} {\int}^{\pi} \left[\frac{{a}^{\mathrm{2}} \sigma\:\mathrm{sin}\:\theta}{\mathrm{2}\epsilon\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} −\mathrm{2}{ax}\:\mathrm{cos}\theta}}\right]{d}\theta \\ $$$$\mathrm{If}\:{a}>{x}\:\mathrm{show}\:\mathrm{that}\:{E}\:=\:\frac{{a}^{\mathrm{2}} \sigma}{\epsilon{x}} \\ $$ Commented by Tinku Tara last…
Question Number 168857 by Sotoberry last updated on 19/Apr/22 Answered by MJS_new last updated on 20/Apr/22 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\sqrt{\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}+\mathrm{1}}}{dx}=\int\frac{\sqrt{{x}−\mathrm{1}}}{{x}^{\mathrm{3}} }{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{{x}−\mathrm{1}}\:\rightarrow\:{dx}=\mathrm{2}\sqrt{{x}−\mathrm{1}}{dt}\right] \\ $$$$=\mathrm{2}\int\frac{{t}^{\mathrm{2}} }{\left({t}^{\mathrm{2}}…
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Question Number 37784 by prof Abdo imad last updated on 17/Jun/18 $${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\:\:\frac{{dx}}{\mathrm{2}{cosx}\:+{cos}\left(\mathrm{2}{x}\right)} \\ $$ Commented by math khazana by abdo last updated on…