Calculating Flux through a Sphere using Divergence Theorem

[CB4]

Evaluate [URL]http://webwork.latech.edu/webwork2_files/tmp/equations/93/91cfe28c766cad38444f0213c651281.png[/URL] where [URL]http://webwork.latech.edu/webwork2_files/tmp/equations/59/a56001472f977192637ea927c607a61.png[/URL] and is the surface of the sphere of radius 6 centered at the origin.

Ok so I started by taking the divF to get 3y^2+3x^2+3z^2. Using polar coordinates I created the integral (from 0 to 2pi) of the integral (from 0 to pi/2) of the integral (from 0 to 6) (3r²sin²(theta)sin²(phi)+3r²cos²(theta)sin²(phi)+3r²cos²(phi)))r²sin(phi) d(phi)d(theta)d(r).

After all of that I simplified my answer down but I keep getting a huge number, 29314.82937, for an answer and it's incorrect. This problem seems very easy so I feel like I'm missing a very obvious step.

 

[Sethric]

If it helps, instead of converting each term, convert them as a group to r^2.

 

[CB4]

That is a good idea, but I still didn't come out with the right answer.

 

[Sethric]

Why are you taking phi from 0 to pi/2? It should be to pi.

 

[CB4]

That is the million dollar question. Thank you very much my friend.