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

Evaluate: [tex]\int[/tex][tex]\int[/tex]G(r)dA

Where G = z

S: x^{2}+ y^{2}+ z^{2}= 9 [tex]z \geq 0[/tex]

2. Relevant equations

Parameterization

x = r sinu cosv

y = r sinu sin v

z = r cos u

3. The attempt at a solution

r(u,v) = (r sinu cosv)i + (r sinu sinv)j + (r cosu)k

r_{u}= (r cosu cosv)i + (-r cos u sinv)j + (-r sinu)k

r_{v}= (-r sinu sinv)i + (r sinu cosv)j + 0k

dA = |r_{u}xr_{v}|

I am not sure if I am approaching this correctly or if I am way off base. My next step was to complete the dot product of z with dA but this does not seem right and I can't find any good examples in my text.

Thank you in advance.

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# Surface Integral of a Sphere (non-divergence)

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