Question Number 33342 by prof Abdo imad last updated on 14/Apr/18 $${let}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{1}}{{x}}\left(\mathrm{1}−\left(\mathrm{1}−\frac{{x}}{{n}}\right)^{{n}} \right){dx}\:{and} \\ $$$${J}_{{n}} \:=\:\int_{\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{x}}\left(\mathrm{1}−\frac{{x}}{{n}}\right)^{{n}} {dx}\:\:,{n}\:{integr}\:{not}\:\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{lim}_{} \:{I}_{{n}}…
Question Number 33339 by prof Abdo imad last updated on 14/Apr/18 $${find}\:\:{lim}_{{n}\rightarrow\infty} \:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{x}^{\mathrm{2}} } \:{sin}^{{n}} {xdx}\: \\ $$ Commented by prof Abdo imad…
Question Number 33340 by prof Abdo imad last updated on 14/Apr/18 $${find}\:{a}\:{equivalent}\:{of} \\ $$$${A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\:\sqrt{\mathrm{1}\:+\left(\mathrm{1}−\frac{{x}}{{n}}\right)^{{n}} }\:\:{dx}\:\left({n}\rightarrow\infty\right) \\ $$ Commented by prof Abdo imad…
Question Number 33338 by prof Abdo imad last updated on 14/Apr/18 $${find}\:{lim}_{{n}\rightarrow\infty} \:\int_{\mathrm{0}} ^{+\infty} \:{tan}^{{n}} {xdx}\:.\: \\ $$ Commented by math khazana by abdo last…
Question Number 33333 by prof Abdo imad last updated on 14/Apr/18 $${let}\:{hive}\:\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\left({sinx}\right)^{{n}} \:{dx} \\ $$$${prove}\:{that}\:\:{I}_{{n}} \:\sim\:\:\sqrt{\frac{\pi}{\mathrm{2}{n}}}\:\left({n}\rightarrow\infty\right) \\ $$$$ \\ $$ Terms of…
Question Number 33334 by prof Abdo imad last updated on 14/Apr/18 $${decompose}\:{F}\left({x}\right)=\:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} \:−\mathrm{1}}\:{imside}\:{R}\left({x}\right)\: \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\:\:\int_{\mathrm{2}} ^{+\infty} \:\:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} \:−\mathrm{1}}\:\:. \\ $$ Commented by prof…
Question Number 33331 by prof Abdo imad last updated on 14/Apr/18 $${calcilate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} } \\ $$ Commented by math khazana by abdo last…
Question Number 33328 by prof Abdo imad last updated on 14/Apr/18 $${find}\:\:\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\mathrm{4}}{\pi}} \:\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){arctanx}\:{dx} \\ $$ Commented by math khazana by abdo last updated…
Question Number 33329 by prof Abdo imad last updated on 14/Apr/18 $${find}\:\:\int\:\:\:\frac{{dx}}{\:\sqrt{\mathrm{4}{x}−{x}^{\mathrm{2}} }}\:. \\ $$ Commented by prof Abdo imad last updated on 19/Apr/18 $${I}\:\:=\:\int\:\:\:\:\:\frac{{dx}}{\:\sqrt{−{x}^{\mathrm{2}}…
Question Number 33327 by prof Abdo imad last updated on 14/Apr/18 $${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dx}}{\mathrm{3}\:+{e}^{−{x}} } \\ $$ Commented by math khazana by abdo last updated…