Question Number 40142 by maxmathsup by imad last updated on 16/Jul/18 $${calculate}\:\:\:\:\int_{−\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{6}}} \:\:\:\frac{\mathrm{1}+{tan}\left({x}\right)}{\mathrm{1}+{sin}\left(\mathrm{2}{x}\right)}{dx} \\ $$$$ \\ $$ Commented by maxmathsup by imad last updated…
Question Number 40143 by maxmathsup by imad last updated on 16/Jul/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\:\:\frac{{tan}\left({x}\right){dx}}{\:\sqrt{\mathrm{2}}{cos}\left({x}\right)\:+\mathrm{2}{sin}^{\mathrm{2}} \left({x}\right)} \\ $$ Commented by math khazana by abdo last updated…
Question Number 40140 by maxmathsup by imad last updated on 16/Jul/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{sin}\left({x}\right){dx}}{{cos}^{\mathrm{2}} {x}\:+{a}^{\mathrm{2}} \:{sin}^{\mathrm{2}} {x}}{dx} \\ $$ Commented by math khazana by abdo…
Question Number 40141 by maxmathsup by imad last updated on 16/Jul/18 $${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\:\frac{{dx}}{\mathrm{3}+{sinx}} \\ $$ Commented by maxmathsup by imad last updated on 19/Jul/18…
Question Number 105673 by I want to learn more last updated on 30/Jul/20 Answered by mathmax by abdo last updated on 30/Jul/20 $$\mathrm{A}\:=\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{15}} \mathrm{f}\left(\mathrm{k}\right)\:=\sum_{\mathrm{k}=\mathrm{1}}…
Question Number 40138 by maxmathsup by imad last updated on 16/Jul/18 $${let}\:\:{a}_{{k}} \:\:\:=\int_{−\frac{\pi}{\mathrm{2}\:}\:+{k}\pi} ^{−\frac{\pi}{\mathrm{2}}\:+\left({k}+\mathrm{1}\right)\pi} \:{e}^{−{t}} \:{cost}\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{a}_{{k}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\mid{a}_{{k}} \mid. \\…
Question Number 40139 by maxmathsup by imad last updated on 16/Jul/18 $${let}\:\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{x}^{{n}} \sqrt{\mathrm{1}−{x}}\:{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}_{\mathrm{0}} \:\:{and}\:{I}_{\mathrm{1}} \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\:\forall{n}\in\:{N}^{\bigstar} \:\:\:\:\left(\mathrm{3}+\mathrm{2}{n}\right)\:{I}_{{n}} =\mathrm{2}{n}\:{I}_{{n}−\mathrm{1}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{I}_{{n}}…
Question Number 40136 by maxmathsup by imad last updated on 16/Jul/18 $${let}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} \:{e}^{−{x}} {dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{\mathrm{1}} \:\:\:{and}\:{A}_{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\:\:{A}_{{n}+\mathrm{1}} =\left({n}+\mathrm{1}\right){A}_{{n}} \:−\frac{\mathrm{1}}{{e}} \\…
Question Number 40134 by maxmathsup by imad last updated on 16/Jul/18 $${calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\:\:\frac{{x}^{\mathrm{3}} }{\left(\mathrm{1}+{x}^{\mathrm{4}} \right)^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup by imad last…
Question Number 40132 by maxmathsup by imad last updated on 16/Jul/18 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{3}} } \\ $$ Commented by maxmathsup by imad last updated…