Question Number 127774 by Bird last updated on 02/Jan/21 $${calculate}\:\:{u}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 02/Jan/21…
Question Number 127775 by Bird last updated on 02/Jan/21 $${prove}\:{that}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}} {lnxdx}=−\gamma \\ $$ Answered by Dwaipayan Shikari last updated on 02/Jan/21 $$\int_{\mathrm{0}} ^{\infty}…
Question Number 127772 by Bird last updated on 02/Jan/21 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{dx}}{\left({cosx}\:+\mathrm{2}{sinx}\right)^{\mathrm{2}} } \\ $$ Answered by mathmax by abdo last updated on 02/Jan/21 $$\mathrm{I}\:=\int_{\mathrm{0}}…
Question Number 127773 by Bird last updated on 02/Jan/21 $${find}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\:\:\int_{{x}} ^{{x}^{\mathrm{2}} } \:\frac{{sh}\left({xt}\right)}{{t}+{x}}{dt} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 127771 by Dwaipayan Shikari last updated on 01/Jan/21 $$\frac{\mathrm{1}}{\mathrm{1}−\frac{\pi^{\mathrm{2}} }{\mathrm{1}+\pi^{\mathrm{2}} −\frac{\mathrm{2}\pi^{\mathrm{2}} }{\mathrm{2}+\pi^{\mathrm{2}} −\frac{\mathrm{3}\pi^{\mathrm{2}} }{\mathrm{3}+\pi^{\mathrm{2}} −\frac{\mathrm{4}\pi^{\mathrm{2}} }{\mathrm{4}+\pi^{\mathrm{2}} −\frac{\mathrm{5}\pi^{\mathrm{2}} }{\mathrm{5}+\pi^{\mathrm{2}} ….}}}}}} \\ $$ Commented by…
Question Number 62234 by aliesam last updated on 18/Jun/19 Answered by tanmay last updated on 18/Jun/19 $$\mathrm{9}\left({x}+{y}\right)=\left({x}+{y}\right)\left({x}^{\mathrm{2}} −{xy}+{y}^{\mathrm{2}} \right) \\ $$$$\left({x}+{y}\right)\left(\mathrm{9}−{x}^{\mathrm{2}} +{xy}−{y}^{\mathrm{2}} \right)=\mathrm{0} \\ $$$${eithdr}\:{x}+{y}=\mathrm{0}\:\:\:{or}\:{x}^{\mathrm{2}}…
Question Number 62232 by aliesam last updated on 18/Jun/19 Commented by maxmathsup by imad last updated on 18/Jun/19 $${we}\:{have}\:\mid\alpha+\beta\:{e}^{{i}\theta} \mid\:=\mid\alpha\:+\beta{cos}\theta\:+{i}\beta{sin}\theta\mid\:=\sqrt{\left(\alpha+\beta{cos}\theta\right)^{\mathrm{2}} \:+\beta^{\mathrm{2}} {sin}^{\mathrm{2}} \theta}\:\Rightarrow \\ $$$${ln}\left(\mid\alpha+{ie}^{{i}\theta}…
Question Number 62228 by behi83417@gmail.com last updated on 17/Jun/19 $$\begin{cases}{\sqrt{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{x}}}+\sqrt{\boldsymbol{\mathrm{a}}−\boldsymbol{\mathrm{y}}}=\mathrm{2}\boldsymbol{\mathrm{a}}}\\{\sqrt{\boldsymbol{\mathrm{a}}−\boldsymbol{\mathrm{x}}}+\sqrt{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{y}}}=\mathrm{2}\boldsymbol{\mathrm{a}}}\end{cases}\:\:\:\:\:\boldsymbol{\mathrm{a}}\in\boldsymbol{\mathrm{R}}. \\ $$ Commented by mr W last updated on 18/Jun/19 $${a}>\mathrm{0} \\ $$$$−{a}\leqslant{x},{y}\leqslant{a} \\ $$$${x}={y}…
Question Number 62227 by behi83417@gmail.com last updated on 17/Jun/19 $$\mathrm{1}.\int\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}^{\mathrm{3}} \:\:}\boldsymbol{\mathrm{dx}}=? \\ $$$$\mathrm{2}.\int\:\:\:\frac{\sqrt{\mathrm{1}−\boldsymbol{\mathrm{tgx}}}}{\boldsymbol{\mathrm{sinx}}}\:\:\boldsymbol{\mathrm{dx}}=? \\ $$$$\mathrm{3}.\int\:\:\:\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} .\boldsymbol{\mathrm{ln}}\left(\mathrm{1}+\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\right)\boldsymbol{\mathrm{dx}}=? \\ $$$$\mathrm{4}.\int\:\:\frac{\boldsymbol{\mathrm{sinx}}}{\mathrm{1}+\boldsymbol{\mathrm{sinx}}+\boldsymbol{\mathrm{sin}}\mathrm{2}\boldsymbol{\mathrm{x}}}\:\boldsymbol{\mathrm{dx}}=? \\ $$ Commented by maxmathsup…
Question Number 62225 by maxmathsup by imad last updated on 17/Jun/19 $${let}\:{j}\:={e}^{\frac{{i}\mathrm{2}\pi}{\mathrm{3}}} \:\:\:{and}\:{P}\left({x}\right)\:=\left(\mathrm{1}+{jx}\right)^{{n}} −\left(\mathrm{1}−{jx}\right)^{{n}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{P}\left({x}\right)\:{at}\:{form}\:{of}\:{arctan} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{roots}\:{of}\:{P}\left({x}\right) \\ $$$$\left.\mathrm{3}\right){factorize}\:{inside}\:{C}\left[{x}\right]\:\:{the}\:{polynome}\:{P}\left({x}\right) \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{P}\left({x}\right){dx} \\…