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Question Number 226101 by Lara2440 last updated on 19/Nov/25 $$\overset{\rightarrow} {\boldsymbol{\mathcal{S}}}\left({u},{v}\right)=\begin{cases}{{r}\centerdot\left(\mathrm{2}+{v}\centerdot\mathrm{sin}\left({u}\right)\right)\mathrm{sin}\left(\mathrm{2}\pi{v}\right)}\\{{rv}\centerdot\mathrm{cos}\left({u}\right)}\\{{r}\centerdot\left(\mathrm{2}+{v}\centerdot\mathrm{sin}\left({u}\right)\right)\mathrm{cos}\left(\mathrm{2}\pi{v}\right)+{r}\centerdot\left(\mathrm{2}{v}−\mathrm{2}\right)}\end{cases} \\ $$$$\mathcal{D}=\left(\mathrm{0}\leq{r}<\infty\:,\:−\pi\leq{u}\leq\pi\:,\:\mathrm{0}\leq{v}\leq\frac{\pi}{\mathrm{2}}\:\right) \\ $$$$\int\int_{\:\mathcal{D}} \:\mathrm{det}\:\overset{\rightarrow} {\boldsymbol{\mathcal{S}}}_{{u}} ×\overset{\rightarrow} {\boldsymbol{\mathcal{S}}}_{{v}} \:\mathrm{d}{V}=?? \\ $$ Terms of Service…

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Question Number 226042 by fantastic2 last updated on 18/Nov/25 Commented by fantastic2 last updated on 18/Nov/25 $${extermely}\:{hard}\:{Question} \\ $$ Commented by mr W last updated…

Question Number 226022 by fantastic2 last updated on 18/Nov/25 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left({x}^{{x}} \right)^{\left({x}^{{x}} \right)^{\left({x}^{{x}} \right)^{…} } } {dx}=? \\ $$ Commented by fantastic2 last updated…

Question Number 225970 by fantastic2 last updated on 17/Nov/25 $$\mathrm{2}^{\mathrm{100}!} \:?\:\mathrm{2}^{\mathrm{100}} !\left[=,<{or}\:>\right] \\ $$ Commented by Ghisom_ last updated on 18/Nov/25 $${b}^{{n}!} \:\mathrm{vs}.\:{b}^{{n}} !\:\:\mathrm{where}\:{b},\:{n}\:\in\mathbb{N}\wedge{b}\geqslant\mathrm{2} \\…