S-F-dS-F-yze-1-xze-2-xye-3-S-x-y-z-2-v-sin-u-sin-2piv-v-cos-u-2-v-sin-u-cos-2piv-2v-2-

Question Number 199736 by MathedUp last updated on 08/Nov/23

∫∫_( S) F^� ∙dS^� F^� =−yze_1 ^� −xze_2 ^� −xye_3 S^� ; ((x^� ),(y^� ),(z^� ) )= ((( (2+v∙sin(u))sin(2πv))),(( v∙cos(u))),(((2+v∙sin(u))cos(2πv)+(2v−2))) )

$$\int\int_{\:\boldsymbol{\mathcal{S}}} \:\hat {\boldsymbol{\mathrm{F}}}\centerdot\mathrm{d}\hat {\boldsymbol{\mathrm{S}}} \\ $$$$\hat {\boldsymbol{\mathrm{F}}}=−{yz}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} −{xz}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} −{xy}\boldsymbol{\mathrm{e}}_{\mathrm{3}} \: \\ $$$$\hat {\boldsymbol{\mathrm{S}}};\:\begin{pmatrix}{\hat {{x}}}\\{\hat {{y}}}\\{\hat {{z}}}\end{pmatrix}=\begin{pmatrix}{\:\:\:\:\:\:\:\:\:\:\left(\mathrm{2}+{v}\centerdot\mathrm{sin}\left({u}\right)\right)\mathrm{sin}\left(\mathrm{2}\pi{v}\right)}\\{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{v}\centerdot\mathrm{cos}\left({u}\right)}\\{\left(\mathrm{2}+{v}\centerdot\mathrm{sin}\left({u}\right)\right)\mathrm{cos}\left(\mathrm{2}\pi{v}\right)+\left(\mathrm{2}{v}−\mathrm{2}\right)}\end{pmatrix} \\ $$

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S-F-dS-F-yze-1-xze-2-xye-3-S-x-y-z-2-v-sin-u-sin-2piv-v-cos-u-2-v-sin-u-cos-2piv-2v-2-

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