Question Number 224798 by Tawa11 last updated on 04/Oct/25 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{arctan}^{\mathrm{2}} \left(\mathrm{x}\right)\:\mathrm{ln}\left(\mathrm{1}\:\:\:−\:\:\:\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 224789 by fkwow344 last updated on 04/Oct/25 $$\mathrm{prove}\:\mathrm{Sphere}\:\mathcal{S};\mathbb{R}^{\mathrm{3}} \rightarrow\mathbb{R} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} ={R}^{\mathrm{2}} \:,\:\mathrm{Euler}\:\mathrm{characteristic}\:\boldsymbol{\chi}=\mathrm{2} \\ $$$$\mathrm{by}\:\mathrm{gauss}-\mathrm{Bonnet}\:\mathrm{theorem} \\ $$$$\mathrm{2}\pi\boldsymbol{\chi}\left(\boldsymbol{\Omega}\right)=\int_{\:\boldsymbol{\Omega}} \:\mathrm{d}{A}\:{K} \\ $$$$\mathrm{Gauss}\:\mathrm{curvature}\:\mathrm{defined}\:\mathrm{as}\:{K}=\frac{\mathrm{det}\:\Pi}{\mathrm{det}\:\mathrm{I}}=\frac{{LN}−{M}^{\mathrm{2}} }{{EG}−{F}^{\mathrm{2}}…
Question Number 224790 by Tawa11 last updated on 04/Oct/25 Commented by Tawa11 last updated on 04/Oct/25 Commented by Tawa11 last updated on 04/Oct/25 $$\mathrm{Am}\:\mathrm{not}\:\mathrm{sure}\:\mathrm{sir} \\…
Question Number 224777 by mr W last updated on 03/Oct/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 224773 by Ismoiljon_008 last updated on 03/Oct/25 Answered by mr W last updated on 03/Oct/25 Commented by mr W last updated on 03/Oct/25…
Question Number 224770 by Abdulazim last updated on 03/Oct/25 $$\:\:\:\left(\mathrm{2}{x}^{\mathrm{3}} +{x}−\mathrm{3}\right)^{\mathrm{3}} =\mathrm{3}−{x}^{\mathrm{2}} \\ $$ Commented by Ghisom_ last updated on 04/Oct/25 $$\mathrm{we}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate} \\ $$ Terms…
Question Number 224771 by mnjuly1970 last updated on 03/Oct/25 $$ \\ $$$$\:\:{K}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sinx}}{{coshx}}\:\left({e}^{−\mathrm{2}{x}} −{e}^{−\mathrm{4}{x}} \right){dx}=?\:\:\:\:\: \\ $$$$\:\: \\ $$ Terms of Service Privacy Policy…
Question Number 224760 by fantastic last updated on 02/Oct/25 $$\mathrm{log}\:_{\mathrm{5}} \left(\mathrm{5}^{\frac{\mathrm{1}}{{x}}} +\mathrm{125}\right)=\mathrm{log}\:_{\mathrm{5}} \mathrm{6}+\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}{x}} \\ $$$${x}=?? \\ $$ Answered by som(math1967) last updated on 02/Oct/25 $$\:{log}_{\mathrm{5}}…
Question Number 224763 by behi834171 last updated on 02/Oct/25 Commented by Ghisom_ last updated on 03/Oct/25 $$\mathrm{min}\:{f}\left({x},\:{y}\right)\:\mathrm{is}\:\approx\mathrm{3}.\mathrm{67113410}\:\mathrm{at} \\ $$$$\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\begin{pmatrix}{\frac{\mathrm{5}\sqrt{\mathrm{6}}−\mathrm{3}\sqrt{\mathrm{5}}}{\mathrm{7}}}\\{\mathrm{3}\sqrt{\mathrm{10}}−\mathrm{5}\sqrt{\mathrm{3}}}\end{pmatrix} \\ $$ Commented by behi834171 last…
Question Number 224753 by Tawa11 last updated on 01/Oct/25 Commented by fantastic last updated on 01/Oct/25 $${wdym}\:{by}\:{magnitude}\:{of}\:{reaction} \\ $$$${is}\:{the}\:{mass}\:{of}\:{the}\:{block}\:{on}\:{inclined} \\ $$$${surface}\:{is}\:\mathrm{7}{kg}? \\ $$ Commented by…