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Surface Integral of a Sphere (nondivergence) 
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#1
Nov1108, 08:20 PM

P: 34

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} x r_{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. 


#2
Nov1108, 10:09 PM

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P: 25,228

You are doing it ok. There's a simpler way to get dA. You know that dV in spherical coordinates is just r^2*sin(u)*du*dv*dr, right? dA over a sphere is just that without the dr. But you should get the same thing by finding the norm of your cross product.



#3
Nov1208, 04:11 AM

Math
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PF Gold
P: 39,488

r= 3 in this problem and you don't use "the dot product of z with dA" because neither is a vector! Just multiply and integrate.



#4
Nov1208, 11:52 AM

P: 34

Surface Integral of a Sphere (nondivergence)
Thank you very much for the help! I believe that I have figured it out now.



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