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…
Question Number 71814 by Aman Arya last updated on 20/Oct/19 $$\int\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cot}\:{x}}{dx} \\ $$ Commented by mathmax by abdo last updated on 20/Oct/19 $${let}\:{I}=\int\:\frac{{dx}}{\mathrm{1}+{cotanx}}\:\Rightarrow{I}=\int\:\frac{{dx}}{\mathrm{1}+\frac{{cosx}}{{sinx}}}\:=\int\frac{{sinx}}{{sinx}\:+{cosx}}{dx} \\ $$$${changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give}\:{I}=\int\:\:\frac{\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 137345 by liberty last updated on 01/Apr/21 $$\ell\:=\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{4}} \sqrt{\mathrm{cos}\:^{\mathrm{3}} \left(\mathrm{2}{x}\right)}\:\mathrm{cos}\:{x}\:{dx}\:=?\: \\ $$ Answered by MJS_new last updated on 01/Apr/21 $$\int\mathrm{cos}^{\mathrm{3}/\mathrm{2}} \:\mathrm{2}{x}\:\mathrm{cos}\:{x}\:{dx}= \\…
Question Number 137341 by EDWIN88 last updated on 01/Apr/21 $$\int\:\frac{{dx}}{\mathrm{e}^{{x}/\mathrm{2}} +{e}^{{x}/\mathrm{3}} +{e}^{{x}/\mathrm{6}} +\mathrm{1}}\:=? \\ $$ Answered by liberty last updated on 01/Apr/21 Terms of Service…
Question Number 71802 by mathmax by abdo last updated on 20/Oct/19 $${find}\:\int\:\:\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}+\mathrm{3}\right)^{\mathrm{2}} \left({x}^{\mathrm{3}} −\mathrm{5}{x}+\mathrm{4}\right)}{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 71801 by mathmax by abdo last updated on 20/Oct/19 $${find}\:\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} \sqrt{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:\:{with}\:{n}\:{integr}\:{natural} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 137328 by mnjuly1970 last updated on 01/Apr/21 Answered by Dwaipayan Shikari last updated on 01/Apr/21 $$−\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {tan}^{\mathrm{2}} \left({x}\right){log}\left({sinx}\right){dx}\:\:\:\:\:\: \\ $$$$=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {log}\left({sinx}\right)−\int_{\mathrm{0}}…
Question Number 71799 by mind is power last updated on 20/Oct/19 Answered by mind is power last updated on 20/Oct/19 $$\mathrm{posted}\:\mathrm{Quation}\:\mathrm{two}\:\mathrm{weeks}\:\mathrm{Ago}−\:\mathrm{nice}\:\mathrm{one}\: \\ $$ Answered by…
Question Number 6248 by FilupSmith last updated on 20/Jun/16 $$\int_{−\infty} ^{\:\infty} {e}^{−{u}} {u}^{{n}} {du}\:=\:??? \\ $$ Commented by 123456 last updated on 20/Jun/16 $$\mathrm{i}\:\mathrm{think}\:\mathrm{that}\:\mathrm{it}\:\mathrm{diverges} \\…