1. The problem statement, all variables and given/known data Find the surface integral of u dot n over S where S is the part of the surface z = x + y2 with z<0 and x>-1, u is the vector field u = (2y+x,-1,0) and n has a negative z component. 2. Relevant equations In the text leading up to the end-of-chapter exercises (where this question arises), n is specified as a unit normal vector. 3. The attempt at a solution The solution claims that ndS = (1,2y,-1)dxdy. But isn't this ignoring the fact that n should be a unit vector? Obviously, the position vector for the surface in parameter form is r = (x,y,x+y2), and n is obtained by taking the partial derivative of r with respect to y, the partial derivative of r with respect to x, and forming the cross product of the two (in that order). But then, shouldn't this resulting vector be divided by the magnitude of the cross product- which, by my calculations happens to be √(2 + 4y2), which is never 1?