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
Since, both the surfaces $H$ and $P$ have same boundary.
This means that the equation of circle is : $x^2+y^2=4$
Stokes' Theorem states that $\iint_{S} curl F \cdot dS=\iint_{C} F \cdot dr$
where, $C$ corresponds to the boundary of the surface oriented counter-clockwise.
So, Stokes' Theorem can be expressed 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.
