Answer
$\iint_{H} curl F \cdot dS=\iint_{P} curl F \cdot dS=\iint_{C} F \cdot dr$;
and $C$ is the circle $x^2+y^2=4$ oriented counter-clockwise.
Work Step by Step
Stokes' Theorem: $\iint_{S} curl F \cdot dS=\iint_{C} F \cdot dr$; and $C$ refers to the boundary of the surface oriented counter-clockwise.
Both the surfaces $H$ and $P$ have the same boundary: the circle $x^2+y^2=4$
So, Stokes' Theorem can be defined as: $\iint_{H} curl F \cdot dS=\iint_{P} curl F \cdot dS=\iint_{C} F \cdot dr$;
and $C$ is the circle $x^2+y^2=4$ oriented counter-clockwise.
