Calculating Surface Integrals Using the Divergence Theorem

[liishii]

Homework Statement

Evaluate the double integral over M (F $$\circ$$ dS) where M is the surface of the sphere of radius 3 centered around the origin. (Sorry! I couldn't figure out how to use math symbols!)

Homework Equations

double integral(F$$\bullet$$dS)=triple integral ($$\nabla$$$$\bullet$$ F)dV due to the divergence thm.

The Attempt at a Solution

I used the divergence theorem and got triple int(3y^2+3x^2+3z^2) dx dy dz with the limits z=-3 to 3, y=-$$\sqrt{}3-z^2$$ to $$\sqrt{}3-z^2$$ , x=-$$\sqrt{}3-y^2-z^2$$ to $$\sqrt{}3-y^2-z^2$$ . I plugged this into wolfram alpha but the answer i get isn't the right answer...

THanks in advance for the help!

 

[Undoubtedly0]

Greetings! Did you try using spherical coordinates? This will make the computation much easier, as well as make any mistakes easy to identify.