Question: Let \(F(x, y, z)=\left[\begin{array}{c}y e^{2 z} \\ x e^{2 z} \\ 2 x y e^{2 z}+3 z^{2}\end{array}\right]\) (as in problems #4, 5, and 6), and let \(S\) be that part of

the paraboloid \(x+9 y^{2}+4 z^{2}=36\) that lies on the side of the yz-plane where \(x>0\). Then \(\iint_{S}(\nabla \times \vec{F}) \cdot \hat{n} d \sigma=\) ?.

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