Question Number 37938 by Fawomath last updated on 19/Jun/18 Commented by abdo.msup.com last updated on 19/Jun/18 $$\left.\mathrm{1}\right)\:{let}\:{I}_{{p}} =\:\int\:{x}^{\mathrm{2}} \left({n}−{x}\right)^{{p}} \:{dx}\:{by}\:{parts} \\ $$$${I}_{{p}} =\:−\frac{\mathrm{1}}{{p}+\mathrm{1}}{x}^{\mathrm{2}} \left({n}−{x}\right)^{{p}+\mathrm{1}} \:\:+\frac{\mathrm{1}}{{p}+\mathrm{1}}\int\:\:\mathrm{2}{x}\:\:\left({n}−{x}\right)^{{p}+\mathrm{1}}…
Question Number 169000 by Skabetix last updated on 22/Apr/22 Answered by haladu last updated on 23/Apr/22 $$=\:\frac{\boldsymbol{\pi}}{\mathrm{4}} \\ $$ Commented by Skabetix last updated on…
Question Number 37922 by gunawan last updated on 19/Jun/18 $${f}\::\:\mathbb{N}\:\rightarrow\:\mathbb{R} \\ $$$${g}\::\:\mathbb{N}\:\rightarrow\:\mathbb{R} \\ $$$${f}\left({n}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} {x}^{{n}} \mathrm{sin}\:{x}\:{dx} \\ $$$${g}\left({n}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} {x}^{{n}} \mathrm{cos}\:{x}\:{dx} \\ $$$$\frac{{f}\left({n}+\mathrm{1}\right)−{f}\left({n}\right)}{{g}\left({n}+\mathrm{1}\right)−{g}\left({n}\right)}=? \\…
Question Number 103454 by bemath last updated on 15/Jul/20 $$\int\:\left({x}^{\mathrm{2}} +\mathrm{2}{x}^{\mathrm{4}} +\mathrm{3}{x}^{\mathrm{6}} \right)\sqrt{\mathrm{1}+{x}^{\mathrm{2}} +{x}^{\mathrm{4}} }\:{dx}\: \\ $$ Answered by bobhans last updated on 15/Jul/20 $${I}=\int{x}\left({x}+\mathrm{2}{x}^{\mathrm{3}}…
Question Number 37912 by gunawan last updated on 19/Jun/18 $$\mathrm{Evaluate}\::\:\mathrm{the}\:\mathrm{Integral} \\ $$$$\int_{-\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\mathrm{3}\:\mathrm{cos}\:\theta} {r}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \theta.\:{dr}\:{d}\theta\: \\ $$ Commented by math khazana by…
Question Number 168978 by MikeH last updated on 22/Apr/22 $$\mathrm{Evaluate}\: \\ $$$$\left(\mathrm{a}\right)\:\int\frac{{t}−\mathrm{2}}{{t}−\mathrm{3}\sqrt{\mathrm{2}{t}−\mathrm{4}}\:+\mathrm{2}}\:{dt}\: \\ $$$$\left(\mathrm{b}\right)\:\int\frac{\mathrm{3}{z}}{\left(\mathrm{1}−\mathrm{4}{z}−\mathrm{2}{z}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dz} \\ $$ Answered by floor(10²Eta[1]) last updated on 22/Apr/22…
Question Number 37902 by math khazana by abdo last updated on 19/Jun/18 $${ind}\:{the}\:{value}\:{of}\:{f}\left({a}\right)\:\:=\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{2}} \:+\sqrt{{a}^{\mathrm{2}} \:+{x}^{\mathrm{2}} }}\:{dx} \\ $$$${witha}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right){calculate}\:{f}^{'} \left({a}\right)\:. \\ $$…
Question Number 37896 by abdo mathsup 649 cc last updated on 19/Jun/18 $${let}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{\left[{x}\right]} }{\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}_{{n}} \:\:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{I}_{{n}} \\…
Question Number 37898 by abdo mathsup 649 cc last updated on 19/Jun/18 $${calculate}\:{f}\left(\lambda\right)\:=\:\int_{\mathrm{0}} ^{+\infty} \:\:{e}^{−\lambda{x}} \:{cos}\left(\pi\left[{x}\right]\right){dx} \\ $$$${with}\lambda>\mathrm{0} \\ $$ Commented by prof Abdo imad…
Question Number 37895 by abdo mathsup 649 cc last updated on 19/Jun/18 $${calculate}\:\:\:{A}_{{n}} =\int_{\mathrm{0}} ^{{n}} \left({x}−\left[\sqrt{{x}}\right]\right){dx}\:{and} \\ $$$${lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$ Answered by tanmay.chaudhury50@gmail.com last…