# Surface Integral of a Sphere (non-divergence)

by Wildcat04
Tags: integral, nondivergence, sphere, surface
 P: 34 1. The problem statement, all variables and given/known data Evaluate: $$\int$$$$\int$$G(r)dA Where G = z S: x2 + y2 + z2 = 9 $$z \geq 0$$ 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 ru = (r cosu cosv)i + (-r cos u sinv)j + (-r sinu)k rv = (-r sinu sinv)i + (r sinu cosv)j + 0k dA = |ru x rv| 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.
 Sci Advisor HW Helper Thanks 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.
 Math Emeritus Sci Advisor Thanks 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.
 P: 34 Surface Integral of a Sphere (non-divergence) Thank you very much for the help! I believe that I have figured it out now.

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