Question Number 35687 by prof Abdo imad last updated on 22/May/18 $${calculate}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\pi} \:\:\:\:\:\frac{{dx}}{\mathrm{1}−{a}\:{cosx}}\:\:{a}\:{from}\:{R}\:. \\ $$$$\left.\mathrm{2}\right)\:{application}\:\:{calculate}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{dx}}{\mathrm{1}−\mathrm{2}{cosx}} \\ $$ Commented by prof Abdo imad…
Question Number 35686 by prof Abdo imad last updated on 22/May/18 $${calculate}\:\:\int_{\sqrt{\mathrm{3}}} ^{+\infty} \:\:\:\:\:\frac{{dx}}{{x}\sqrt{\:\mathrm{2}+{x}^{\mathrm{2}} }}\:. \\ $$ Commented by prof Abdo imad last updated on…
Question Number 35685 by prof Abdo imad last updated on 22/May/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:{x}\:{artan}\left(\mathrm{2}{x}+\mathrm{1}\right){dx} \\ $$ Commented by prof Abdo imad last updated on 23/May/18…
Question Number 101220 by Ar Brandon last updated on 01/Jul/20 $$\int\int_{\mathrm{D}} \sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\mathrm{dxdy}\:\:\:\mathcal{D}=\begin{cases}{\left(\mathrm{x},\mathrm{y}\right)\in\mathbb{R},\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \geqslant\mathrm{2y},\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \leqslant\mathrm{1}}\\{\mathrm{x}\geqslant\mathrm{0}\:,\:\mathrm{y}\geqslant\mathrm{0}}\end{cases} \\ $$ Answered by Ar Brandon last…
Question Number 35683 by prof Abdo imad last updated on 22/May/18 $${find}\:\int\:\:{x}^{\mathrm{2}} {ln}\left({x}^{\mathrm{6}} −\mathrm{1}\right){dx} \\ $$ Commented by prof Abdo imad last updated on 30/May/18…
Question Number 35684 by prof Abdo imad last updated on 22/May/18 $${calculate}\:{I}\:\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{e}^{\mathrm{2}{t}} \:{ln}\left(\mathrm{1}+{e}^{{t}} \right){dt} \\ $$ Commented by prof Abdo imad last updated…
Question Number 35682 by prof Abdo imad last updated on 22/May/18 $${let}\:{F}\left({x}\right)\:=\:\int_{{x}\:+\mathrm{1}} ^{{x}^{\mathrm{2}} \:+\mathrm{1}} \:\:\:{arctan}\left(\mathrm{1}+{t}\right){dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\frac{\partial{F}}{\partial{x}}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:\:{find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:{F}\left({x}\right)\:. \\ $$ Commented by tanmay.chaudhury50@gmail.com…
Question Number 35681 by prof Abdo imad last updated on 22/May/18 $${find}\:\:\int\:{arctan}\left({x}\right){dx} \\ $$ Commented by prof Abdo imad last updated on 23/May/18 $${let}\:{integrate}\:{by}\:{parts}\:{u}^{'} \:=\mathrm{1}\:{and}\:{v}={arctan}\left({x}\right)…
Question Number 35680 by prof Abdo imad last updated on 22/May/18 $${by}\:{using}\:{residus}\:{theorem}\:{calculate} \\ $$$${W}_{{n}} \:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:{cos}^{\mathrm{2}{n}} {t}\:{dt}\:\:\left(\:\:{wallis}\:{integal}\right)\:{n}\:{integr} \\ $$$${natural}\:. \\ $$ Terms of Service…
Question Number 35678 by abdo imad last updated on 21/May/18 $${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{tx}^{\mathrm{2}} } \:{arctan}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }{dx}\:{with}\:{t}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{study}\:{the}\:{existencte}\:{of}\:{f}\left({t}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:{f}^{'} \left({t}\right) \\ $$$$\left.\mathrm{3}\right){find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({t}\right). \\…