Question

Doing a triple integral dealing with Divergence in Spherical coordinates, just want to make sure everything is right so far.

Answer 1

http://i.imgur.com/Ae4obGd.png

Answer 2

Just need to insert the Jacobian/integrating factor for Spherical coordinates in there, along with the 3x converted to spherical; but is the general setup right?

Answer 3

You need to replace 3x by \[3 x=3 \cos (\theta ) \sin (\phi )
\]

Answer 4

and
\[
dxdydz= \rho ^2 \sin (\phi )d\phi d\theta d\rho
\]

Answer 5

Alright, cool, but the setup is otherwise correct? I'm going to finish it now.

Answer 6

http://i.imgur.com/uZ1iD6o.png

Answer 7

http://i.imgur.com/kJTwPQR.png

Answer 8

I ended up getting 2pi, but the answer is 3pi.

Answer 9

Sorry, there was a type
\[
3 x=3 \rho \cos (\theta ) \sin (\phi )
\]

Answer 10

\[
\int_0^{\frac{\pi }{2}}
\left(\int_0^{\frac{\pi }{2}}
\left(\int_0^2 3 \rho ^3 \cos (\theta
) \sin ^2(\phi ) \, d\rho \right) \,
d\theta \right) \, d\phi =3 \pi
\]