Hello !

Please consider my post with care since I am not a specialist !

What I can say is that I agree with you for what concerns the strip (integral = 0) but not for the 2 circles.

For the bottom circle, you must integrateF.nds on the surface defined by x²+y²<1 and z=0. You haveF.n=0 becausen=-kandFhas coordinate 0 on vectork(z=0)

For the top circle, you must integrateF.nds on the surface defined by x²+y²<1 and z=3. You haveF.nds = (3(x^2+y^2)^3 / ( [1 + (x^2 + y^2)^4 ]^4)

I hope that I am not wrong ...