Question Number 159960 by tounghoungko last updated on 23/Nov/21 $$\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{3}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{4}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}}\:{dx}\:=?\: \\ $$ Answered by MJS_new last updated on 23/Nov/21 $$\underset{\mathrm{0}}…
Question Number 28890 by abdo imad last updated on 31/Jan/18 $$\left.\mathrm{1}\right)\:{prove}\:{that}\:\forall\:{x}\geqslant\mathrm{0}\:\:\:{x}\:−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\leqslant{ln}\left(\mathrm{1}+{x}\right)\leqslant{x} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\prod_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{1}\:+\:\frac{\mathrm{1}}{{k}^{\mathrm{2}} +{n}^{\mathrm{2}} }\right)^{{n}} . \\ $$ Terms of Service…
Question Number 28889 by abdo imad last updated on 31/Jan/18 $${find}\:\:{I}\:\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} {ln}\left({x}−{e}^{{i}\theta} \right){d}\theta\:\:\:\:{and}\:{xfromR}\:{and}\:{x}^{\mathrm{2}} \neq\mathrm{1}. \\ $$ Commented by abdo imad last updated on 02/Feb/18…
Question Number 28886 by abdo imad last updated on 31/Jan/18 $${find}\:\int\:\:\:\frac{{x}}{{cos}^{\mathrm{2}} {x}}{dx}. \\ $$ Answered by mrW2 last updated on 01/Feb/18 $$\:\int\:\:\:\frac{{x}}{{cos}^{\mathrm{2}} {x}}{dx} \\ $$$$=\int{x}\:{d}\left(\mathrm{tan}\:{x}\right)…
Question Number 28887 by abdo imad last updated on 31/Jan/18 $${find}\:\int\:\:{arcsin}\left(\sqrt{\frac{{x}}{{x}+\mathrm{2}}}\right){dx}. \\ $$ Commented by abdo imad last updated on 02/Feb/18 $${let}\:{use}\:{the}\:{ch}.{arcsin}\left(\sqrt{\:\frac{{x}}{{x}+\mathrm{1}}}\:\right)={t}\:\Leftrightarrow\sqrt{\frac{{x}}{{x}+\mathrm{1}}}\:={sint} \\ $$$$\Leftrightarrow\frac{{x}}{{x}+\mathrm{1}}={sin}^{\mathrm{2}} {t}\:\Leftrightarrow{x}={xsin}^{\mathrm{2}}…
Question Number 28888 by abdo imad last updated on 31/Jan/18 $${find}\:\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{dx}}{\mathrm{1}+{cos}^{\mathrm{2}} \left({nx}\right)}\:{with}\:{n}\in\:{N}^{\bigstar} . \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28885 by abdo imad last updated on 31/Jan/18 $${find}\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{{t}\:+\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}\:. \\ $$ Commented by abdo imad last updated on 02/Feb/18 $${let}\:{put}\:{I}=\:\int_{−\mathrm{1}}…
Question Number 94418 by niroj last updated on 18/May/20 $$\:\mathrm{1}.\mathrm{F}\boldsymbol{\mathrm{ind}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\theta}\:\mathrm{in}\:\mathrm{Mean}\:\mathrm{Value}\:\mathrm{theorem} \\ $$$$\:\mathrm{f}\left(\mathrm{x}+\mathrm{h}\right)=\:\mathrm{f}\left(\mathrm{x}\right)+\mathrm{hf}^{\:'} \left(\mathrm{x}+\theta\mathrm{h}\right),\:\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{x}} \\ $$$$\:\:\mathrm{2}.\mathrm{If}\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\:\:\:\:+\sqrt{\mathrm{1}−\mathrm{y}^{\mathrm{2}} }\:\:\:=\:\mathrm{k}\left(\mathrm{x}−\mathrm{y}\right)\:\mathrm{prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\sqrt{\mathrm{1}−\mathrm{y}^{\mathrm{2}} }}{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}. \\ $$$$\:\mathrm{3}.\:\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}: \\ $$$$\:\:\:\mathrm{x}^{\mathrm{2}}…
Question Number 28884 by abdo imad last updated on 31/Jan/18 $${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:{cost}\:{ln}\left({tant}\right){dt}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28882 by abdo imad last updated on 31/Jan/18 $${find}\:\int_{−\pi} ^{\pi} \:\:\:\frac{\mathrm{2}{dt}}{\mathrm{2}+{sint}\:+{cost}}\:. \\ $$ Commented by abdo imad last updated on 02/Feb/18 $${let}\:{use}\:{the}\:{ch}.\:{e}^{{it}} ={z}…