(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let D be an area in R^3 and S be its surface. D fulfills the Divergence theorem. Let N be the unit normal on S and let the volume, V, be known. Let [tex] (\overline{x},\overline{y}, \overline{z}) [/tex] coordinates of the centre of mass of D be known (and the density delta is constant).

Lets define three vector fields:

[tex] F = (x)i + (y)j + (x)k [/tex]

[tex] G = (xz)i + (2yz)j + (2z^2)k [/tex]

[tex] H = (y^2)i + (2xy)j + (xz)k [/tex]

Find a formula for:

[tex] \int\int_S F\bullet N dS, \int\int_S F\bullet N dS, \int\int_S F\bullet N dS [/tex]

where you use V, [tex] (\overline{x},\overline{y}, \overline{z}) [/tex] !!

2. Relevant equations

Divergence theroem states:

[tex] \int\int_R div F dA = \oint_C F\bullet\widehat{N}ds [/tex]

3. The attempt at a solution

divF is easily found but that doesn't tell me anything at the moment so there is nothin special going on really because I'm completely clueless what to do with the volume and the centre of mass. Any hints would be great.

Thanks in advanced and forgive my english.

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# The divergence theorem.

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