Question Number 137419 by mnjuly1970 last updated on 02/Apr/21 $$\:\:\:\:\:\:\:………{mathematical}\:\:\:\:….\:\:\:{analysis}…….. \\ $$$$\:\:\:\:\:\:\:{evaluate}…. \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{e}^{\mathrm{2}\pi{x}} −{e}^{\pi{x}} }{{x}\left(\mathrm{1}+{e}^{\mathrm{2}\pi{x}} \right)\left(\mathrm{1}+{e}^{\pi{x}} \right)}{dx}=\lambda\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left(\Gamma\left({x}\right){dx}\right. \\ $$$$\:\:\:\:\:\:\:\:\:\:\lambda\:=\:??? \\…
Question Number 6343 by sanusihammed last updated on 24/Jun/16 $$\int{x}^{\mathrm{3}} \:\sqrt{\mathrm{1}\:−\:{x}}\:\:{dx} \\ $$ Answered by nburiburu last updated on 24/Jun/16 $${by}\:{substitution}\:{t}=\sqrt{\mathrm{1}−{x}}\Rightarrow{x}=\mathrm{1}−{t}^{\mathrm{2}} \\ $$$${dx}=−\mathrm{2}{t}\:{dt} \\ $$$${I}=\int\left(\mathrm{1}−{t}^{\mathrm{2}}…
Question Number 6333 by FilupSmith last updated on 24/Jun/16 $${I}=\int_{\mathrm{0}} ^{\:{n}} \lfloor{x}\rfloor\lceil{x}\rceil{dx},\:\:{n}\in\mathbb{Z} \\ $$ Commented by nburiburu last updated on 24/Jun/16 $${I}=\underset{{i}=\mathrm{0}} {\overset{{n}} {\sum}}{i}\left({i}+\mathrm{1}\right) \\…
Question Number 71864 by Learner-123 last updated on 21/Oct/19 $${Draw}\:{the}\:{graph}\:{of}\:: \\ $$$${x}=\mid{y}\mid\:\sqrt{\mathrm{1}−{y}^{\mathrm{2}} } \\ $$ Commented by MJS last updated on 21/Oct/19 $$\mathrm{well},\:\mathrm{just}\:\mathrm{draw}\:\mathrm{it}? \\ $$$$\mathrm{table}…
Question Number 137397 by mnjuly1970 last updated on 02/Apr/21 $$\:…….\mathscr{A}{dvanced}\:…\:\:…\:\:…\:\mathscr{C}{alculus}……. \\ $$$$\:{simplify}\:::: \\ $$$$\:\Omega_{{n}} =\underset{{k}=\mathrm{1}} {\overset{\mathrm{2}{n}+\mathrm{1}} {\sum}}{log}\left(\mathrm{1}+{tan}\left(\frac{{k}\pi}{\mathrm{4}\left(\mathrm{2}{n}+\mathrm{1}\right)}\right)\right) \\ $$$$\:{moreover}\:,\:\:\:\:{find}\:{the}\:{value}\:{of}:: \\ $$$$\Omega=\:{lim}_{{n}\rightarrow\infty} \frac{\Omega_{{n}} }{{n}}\:=??? \\ $$…
Question Number 71850 by SmNayon11 last updated on 21/Oct/19 $$\int\mathrm{ln}\left(\mathrm{x}^{\mathrm{x}^{\mathrm{x}} } .\mathrm{e}^{\mathrm{x}^{\mathrm{x}} } \right)\mathrm{dx}=? \\ $$ Answered by MJS last updated on 21/Oct/19 $$\int\mathrm{ln}\:\left({x}^{{x}^{{x}} }…
Question Number 71831 by ahmadshahhimat775@gmail.com last updated on 20/Oct/19 Commented by kaivan.ahmadi last updated on 20/Oct/19 $${hi}\:{mr}\:{ahmadi} \\ $$$${where}\:{are}\:{you}\:{from}? \\ $$ Commented by Abdo msup.…
Question Number 137359 by rexford last updated on 01/Apr/21 Answered by Ar Brandon last updated on 01/Apr/21 $$\mathcal{I}=\int_{\sqrt[{\mathrm{3}}]{\mathrm{log3}}} ^{\sqrt[{\mathrm{3}}]{\mathrm{log4}}} \frac{\mathrm{x}^{\mathrm{2}} \mathrm{sinx}^{\mathrm{3}} }{\mathrm{sinx}^{\mathrm{3}} +\mathrm{sin}\left(\mathrm{log12}−\mathrm{x}^{\mathrm{3}} \right)}\mathrm{dx} \\…
Question Number 71816 by psyche last updated on 20/Oct/19 $${suppose}\:{that}\:{f}\:{is}\:{continuous}\:{and}\:{differentiable}\:{in}\:\left({a},{b}\right)\:{if}\:{f}'\left({x}\right)\:=\mathrm{0}\:,\forall\:{x}\in\left({a},{b}\right)\:{then}\:{show}\:{that}\:{f}\:{is}\:{constant}\:{on}\:\left[{a},{b}\right]. \\ $$ Answered by mind is power last updated on 20/Oct/19 $$\mathrm{assum}\:\mathrm{f}\:\mathrm{is}\:\mathrm{not}\:\mathrm{consrante} \\ $$$$\exists\mathrm{x},\mathrm{y}\:\mathrm{suche}\:\mathrm{that}\:\mathrm{1}\geqslant\mathrm{y}\neq\mathrm{x}\geqslant\mathrm{0}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\neq\mathrm{f}\left(\mathrm{y}\right) \\…
Question Number 71813 by mathmax by abdo last updated on 20/Oct/19 $$\left.\mathrm{1}\right){calculate}\:{F}\left({a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {arctan}\left(\mathrm{1}+{a}\:{cosx}\right){dx} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{valeur}\:{of}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{arctan}\left(\mathrm{1}+\sqrt{\mathrm{2}}{cosx}\right){dx} \\ $$ Terms of Service Privacy Policy…