Verify Gauss Divergence Theorem ∭∇.F dxdydz=∬F. NdA
Where the closed surface S is the sphere x^2+y^2+z^2=9 and the vector field F = xz^2i+x^2yj+y^2zk
I have tried to solve the left hand side which appear to be (972*pi)/5
However, I cant seems to solve the right hand side to get the same answer.
I substitute x = 3sin(theta)cos(phi), y=3sin(theta)sin(phi), z=3cos(theta)
then I used ∫(0-2pi)∫(0-pi) F. N dθdφ
I got the final answer as (324*pi)/5 which does not match with left hand side.
Hope anyone can help here plz. Thanks!