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Use the Divergence Theorem to evaluate

$$\iint_S x^2y^2+y^2z^2+z^2x^2 dS$$

where $S$ is the surface of the sphere $x^2+y^2+z^2=1$.

So the divergence of F is $2y^2x+2z^2y+2x^2z$. Then I tried to integrate using spherical coordinates, but the integral seemed to be very exhausting. Is there a better way to do it?

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    What's $\mathbf F$?2012-11-09
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    By **F** I meant **F** =P(x,y,z)+Q(x,y,z)+R(x,y,z)=x^2 y^2 + y^2 z^2 + z^2 x^22012-11-09
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    That's a scalar; it doesn't have a divergence.2012-11-09

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