Question Number 30215 by abdo imad last updated on 18/Feb/18 $${let}\:{give}\:{J}\left({x}\right)=\:\frac{\mathrm{1}}{\pi}\:\int_{\mathrm{0}} ^{\pi} {cos}\left({xcost}\right){dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{J}^{'} \:{and}\:{J}^{''} \:{in}\:{form}\:{of}\:{integrals} \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:{J}^{'} \left({x}\right)=\frac{−{x}}{\pi}\:\int_{\mathrm{0}} ^{\pi} \:{sin}^{\mathrm{2}} {t}\:{cos}\left({xcost}\right){dt}\:{and}\:{J}\:{is} \\ $$$${solution}\:{of}\:{d}.{e}.\:\:{xy}^{''}…
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Question Number 95738 by bobhans last updated on 27/May/20 $$\int\:\frac{\mathrm{p}−\mathrm{tan}\:\mathrm{x}}{\mathrm{p}+\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$ Commented by PRITHWISH SEN 2 last updated on 27/May/20 $$\frac{\mathrm{pcosx}−\mathrm{sin}\:\mathrm{x}}{\mathrm{pcos}\:\mathrm{x}+\mathrm{sin}\:\mathrm{x}}\:=\:\frac{\mathrm{m}\left(\mathrm{cos}\:\mathrm{x}−\mathrm{psin}\:\mathrm{x}\right)+\mathrm{n}\left(\mathrm{pcos}\:\mathrm{x}+\mathrm{sin}\:\mathrm{x}\right)}{\mathrm{pcos}\:\mathrm{x}+\mathrm{sin}\:\mathrm{x}} \\ $$$$\mathrm{m}=\frac{\mathrm{2p}}{\mathrm{1}+\mathrm{p}^{\mathrm{2}} }…
Question Number 161265 by mathlove last updated on 15/Dec/21 Commented by amin96 last updated on 15/Dec/21 $${OMG}\left(\:\:\:{e}^{{x}} ={u}\:\:{e}^{{u}} ={t}\:\:\:{e}^{{t}} ={v}………….\right. \\ $$ Commented by MJS_new…
Question Number 95722 by rb222 last updated on 27/May/20 $${use}\:{cylinder}\:{ring}\:{method} \\ $$$$ \\ $$$${y}\:=\:\mathrm{2}{x}−\mathrm{1} \\ $$$${y}\:=\:−\mathrm{2}{x}\:+\:\mathrm{3} \\ $$$${x}\:=\:\mathrm{2}\: \\ $$$$ \\ $$$${y}−{axis}\: \\ $$$$ \\…
Question Number 161256 by cortano last updated on 15/Dec/21 $$\:{Given}\:{f}\left({x}\right)={f}\left({x}+\mathrm{2}\right),\:\forall{x}\in\mathbb{R} \\ $$$$\:{If}\:\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}{f}\left({x}\right){dx}=\:{p}\:{then}\:\underset{\mathrm{0}} {\overset{\mathrm{2020}} {\int}}{f}\left({x}+\mathrm{2}{a}\right){dx}=? \\ $$$$\:{for}\:{a}\in\mathbb{Z}^{+} \\ $$ Answered by talminator2856791 last updated…
Question Number 30185 by abdo imad last updated on 17/Feb/18 $${let}\:\:{I}=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{sinx}}{\:\sqrt{\mathrm{1}+{sinxcosx}}}{dx}\:{and} \\ $$$${J}=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{cosx}}{\:\sqrt{\mathrm{1}+{sinx}\:{cosx}}}\:{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}\:+{J} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{I}\:{and}\:{J}. \\ $$ Terms of…
Question Number 30182 by abdo imad last updated on 17/Feb/18 $${find}\:\int_{\mathrm{2}} ^{\mathrm{3}} \:\:\:\frac{\sqrt{{x}+\mathrm{1}}}{{x}\sqrt{\mathrm{1}−{x}}}{dx}\:. \\ $$ Commented by abdo imad last updated on 21/Feb/18 $${let}\:{put}\:\sqrt{\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}}\:={t}\:\Leftrightarrow\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\:={t}^{\mathrm{2}} \:\:\Leftrightarrow{x}+\mathrm{1}=−{t}^{\mathrm{2}}…
Question Number 30184 by abdo imad last updated on 17/Feb/18 $${find}\:\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{2}} \:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){arctanx}\:{dx}\:.\:\left({arctan}={tan}^{−\mathrm{1}} \right). \\ $$ Commented by abdo imad last updated on 20/Feb/18…
Question Number 30181 by abdo imad last updated on 17/Feb/18 $${find}\:\:\int\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{3}} \:+{x}^{\mathrm{6}} }\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com