Choosing the normal in a scalar field over sphere
EDIT: I am not allowed to use Gauss in this problem
Solve the surface integral of (2x+x^3*z)*ndS over the surface of the sphere with origo in (0,1,0) with radius 1. n points outward.
My attempt at solution:
I have no attempt made because I get stuck at the fact that (2x+x^3*z) is multiplied by a vector n. For this to be a viable solution I assume that n can only be in one directon x,y or z otherwise I have to integrate over a vector and that does not feel right for me.
What would n be for a sphere and why cant I find any information anywhere what it might be?