Ok i have done majority of the working for this, but get a bit stuck on a conventional basis. Though i may of gone wrong.

My attempt:Evaluate the flux

of the vector field

.

Where

is the radius vector and r is its modulus, through the surface of a sphere of radius R.

where

Surface must be :

Im not suppose to use divergence theorem for this (as it asks to prove both ways)

Hence:

sub in sphereical polar coordinates etc:

If you dot it with the integration above i get:

This is where i am stuck, there is no reason why i picked the k direction to be dotted with n, by doing so i get but it does matter in terms of the integral, dA will have to be in terms of dr but the other can be or both of which have different limits (2pi, 0 and pi, 0) in which case the result will change

Any help is appreciated