Question Number 204902 by pticantor last updated on 01/Mar/24 $$\boldsymbol{{calculate}}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\boldsymbol{{x}}\left(\mathrm{1}−\boldsymbol{{x}}\right)}\boldsymbol{{dx}} \\ $$ Answered by witcher3 last updated on 01/Mar/24 $$\mathrm{y}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} −\mathrm{x}=\mathrm{0}\Leftrightarrow\mathrm{y}^{\mathrm{2}} +\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}}…
Question Number 204866 by mathlove last updated on 29/Feb/24 $$\int\:\frac{{x}+\mathrm{3}}{{x}^{\mathrm{2}} \sqrt{\mathrm{2}{x}+\mathrm{3}}}\:{dx}=? \\ $$ Answered by Frix last updated on 29/Feb/24 $$\int\frac{{x}+\mathrm{3}}{{x}^{\mathrm{2}} \sqrt{\mathrm{2}{x}+\mathrm{3}}}{dx}\:\overset{{t}=\frac{\sqrt{\mathrm{2}{x}+\mathrm{3}}}{{x}}} {=}−\int{dt}=−{t}=−\frac{\sqrt{\mathrm{2}{x}+\mathrm{3}}}{{x}}+{C} \\ $$…
Question Number 204802 by Faetmaaa last updated on 27/Feb/24 $$\mathrm{Wi}-\mathrm{Fi}\:\mathrm{code}\:\mathrm{problem}: \\ $$$$\int_{−\mathrm{2}} ^{\:\mathrm{2}} \left({x}^{\mathrm{3}} \mathrm{cos}\left(\frac{{x}}{\mathrm{2}}\right)+\frac{\mathrm{1}}{\mathrm{2}}\right)\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }\mathrm{d}{x} \\ $$ Answered by TonyCWX08 last updated on 28/Feb/24…
Question Number 204705 by Mummyjay last updated on 25/Feb/24 $$\boldsymbol{{evalute}}\:\int_{\mathrm{0}} ^{\infty} \mathrm{2}^{−\sqrt{\boldsymbol{{tanx}}}} \boldsymbol{{dx}} \\ $$ Commented by TonyCWX08 last updated on 27/Feb/24 $${Undefined} \\ $$…
Question Number 204706 by Mummyjay last updated on 25/Feb/24 $$\boldsymbol{{evaluate}}\:\int_{\mathrm{0}} ^{\infty} \mathrm{2}^{−\boldsymbol{\Gamma}\left(\boldsymbol{{x}}\right)} \boldsymbol{{dx}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 204707 by Mummyjay last updated on 25/Feb/24 $$\boldsymbol{{integrate}}\:\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{{e}}^{−\boldsymbol{{x}}^{\mathrm{2}} } }{\mathrm{1}+\boldsymbol{{e}}^{\boldsymbol{{x}}} }\boldsymbol{{dx}} \\ $$ Answered by witcher3 last updated on 26/Feb/24 $$\Omega=\int_{\mathrm{0}}…
Question Number 204645 by cortano12 last updated on 24/Feb/24 $$\:\:\mathrm{Let}\:{f}\::\:\left[\:\bar {\mathrm{1}}\infty\right)\:\rightarrow\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{differentiable}\: \\ $$$$\:\mathrm{function}\:\mathrm{such}\:\mathrm{that}\:{f}\left(\mathrm{1}\right)=\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{and}\: \\ $$$$\:\mathrm{3}\underset{\mathrm{1}} {\overset{\mathrm{x}} {\int}}\:{f}\left({t}\right)\:{dt}\:=\:{x}\:{f}\left({x}\right)−\frac{{x}^{\mathrm{3}} }{\mathrm{3}}\:,\mathrm{x}\in\left[\mathrm{1},\infty\right)\: \\ $$$$\:\mathrm{find}\:\mathrm{tbe}\:\mathrm{value}\:\mathrm{of}\:{f}\left({e}\right)\: \\ $$ Commented by universe…
Question Number 204573 by MathedUp last updated on 22/Feb/24 $$\mathrm{How}\:\mathrm{Can}\:\mathrm{derive}\:\mathrm{LambertW}\left({z}\right)\:\mathrm{in}\:\mathrm{the} \\ $$$$\:\mathrm{Form}\:\mathrm{of}\:\mathrm{integral}??? \\ $$$$\mathrm{W}\left({z}\right)=\frac{\mathrm{1}}{\pi}\int_{\mathrm{0}} ^{\:\pi} \:\mathrm{ln}\left(\mathrm{1}+\frac{{z}\centerdot\mathrm{sin}\left({t}\right)}{{t}}{e}^{{t}\centerdot\mathrm{cot}\left({t}\right)} \right)\mathrm{d}{t}\:,\:{z}\in\left[−\frac{\mathrm{1}}{{e}},\infty\right) \\ $$$$\mathrm{Or}\:\mathrm{Similar}\:\mathrm{to}\:\mathrm{the}\:\mathrm{example}.\mathrm{LambertW}\left({z}\right) \\ $$$$\mathrm{How}\:\mathrm{other}\:\mathrm{Functions}\:\mathrm{can}\:\mathrm{be}\:\mathrm{Derived}\:\mathrm{in}\:\mathrm{Integral}\:\mathrm{Form} \\ $$ Commented by…
Question Number 204569 by pticantor last updated on 21/Feb/24 $$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\: \\ $$$$\boldsymbol{{I}}=\int_{\mathrm{0}} ^{+\infty} \boldsymbol{{ln}}\left(\mathrm{1}+\boldsymbol{{e}}^{−\boldsymbol{{x}}} \right)\boldsymbol{{dx}}\:\boldsymbol{{nowing}}\:\boldsymbol{{that}}\: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}\frac{\mathrm{1}}{\boldsymbol{{n}}^{\mathrm{2}} }=\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$ Answered by…
Question Number 204522 by universe last updated on 20/Feb/24 Commented by witcher3 last updated on 20/Feb/24 $$\phi'\left(\mathrm{y}\right)\:\:\mathrm{not}\:\mathrm{mor}\:\mathrm{information}\:\mathrm{about}\:\phi\:\mathrm{finction}? \\ $$$$ \\ $$ Commented by universe last…