Calculate the surface integral of the vector field a=xy i + (x+1) j + xz^2 k over a square in the xy-plane with length 1 and whose unit normal points in the positive direction of the z axis.
This is the problem. There are many different types of surface integrals. Though since it's a vector field I should assume that they're asking for an integral of the type I = ∫ a [itex]\cdot[/itex] dS, where a and dS are both vectors. Is that right?
The Attempt at a Solution
I'm really not sure, as my book's examples on these are quite poor. I think what I want to find is a general expression for a small vector area in the square. Is that just given by dydx times the unit normal to the xy-plane?
Please help :)