We are given the vector field $F(x,y,z)=[2z+y, 2x+z, 2ycos(z)]$
A surface S is composed of two parts. One part $S_1$ given by $z=x^2+y^2$, for $0\leq z\leq4$ and $0 \leq y$. The second part $S_2$ is given by $x^2 \leq z \leq 4$ for $y=0$. Let C be the edge of S, oriented counterclockwise seen from above.
a) Sketch the surface S and show the orientation of C on the sketch.
b) Based on the parameterization of C calculate $\oint_C F\bullet \,dr$
c)Let S have an orientation that is consistent with the orientation of C, and let N be the external normal vector to . Find $\iint_S curl(F) \bullet N dS$
So I have problems visualiazing how the surface S actually look like. For $S_1$ I know that this must be a parabola with height 4. Since $y\geq0$ this must be half of a parabola (that part lying over the first and second quadrant. For the surface $S_2$ however, I have now idea how it looks like. The inequality makes me a bit confused to be honest. I would really appreciate some help understanding how S looks like. I guess that if I know the surface and the edge of it, both b) and c) should give the same answer given Stokes theorem?