Determine the value of the integral ∬S(∇×F)⋅dS\iint_S (\nabla \times \mathbf{F}) \cdot d\mathbf{S}∬S(∇×F)⋅dS where F=⟨z,x,y⟩\mathbf{F} = \langle z, x, y \rangleF=⟨z,x,y⟩ and SSS is the paraboloid z=1−x2−y2z = 1 - x^2 - y^2z=1−x2−y2 for z≥0z \geq 0z≥0.
−π-\pi−π
π\piπ
2π2\pi2π
000