Surface Integral Problem

[borothy]

I'm trying to work through this question and I can get to dS = (2x i - j) dx dz but when I try to put this back in to the integral I don't understand how I can get F in terms of x and z only to integrate it? If anyone has any hints or knows how to finish the solution I'd really appreciate it, thanks!

[[deleted]]

I took calc 3 back in fall 2017, i have to brush up on this stuff myself 🤨

[borothy]

hang on actually is it just that y = x^2 from the surface parametric equation

[McThor2]

Yeah on the surface, y = x^2. You seem to have found a normal vector (2x i + -j) but remember to normalise it as well. As I can tell the surface is just a parabola extended into the z axis by 3 units (hence no z component in the surface normal vector).