I must verify the divergence theorem in the following case :
. And is the surface of the sphere .
My attempt :
I calculate the right hand side : .
So 3 times the volume of a sphere with radius , hence the triple integral is worth .
Now comes the problems. I ain't able to calculate .
A normal unit vector to the sphere is .
So the double integral is worth . And I'm stuck here because I have 3 variables ( , and ) but a double integral instead of a triple one.
I know I could solve the problem faster using spherical coordinates, but for the sake of my comprehension let's do it via Cartesian coordinates please.
Do you have any idea how could I continue, in order to reach the ?