Verify the divergence theorem for F(x,y,z) = (x,y,2z^2) and T is the region bounded by the paraboloid z=x^2+y^2 and the plane z=1.
F(ds) = div(F)dV
The Attempt at a Solution
I have successfully evaluated the integral and come up with an answer:
div(F) = x/dx + y/dy + 2z^2/dz = 2+4z
Cylindrical limits of integration:
z: r^2 to 1
r: 0 to 1
theta: o to 2(pi)
I found the answer to be 7/3 * pi.
How do I verify this? Do I need to do any more to do so? Please advise ASAP! Thanks!