Use Stokes’ Theorem to calculate $\iint_{S} \nabla \times V· dS$ on the given paraboloid 

Let $S$ be the paraboloid $z = \frac{x^2 + y^2}{4}$ for $z \leq4$ oriented with upward normal vector. Use Stokes’ Theorem to calculate $\iint_{S} \nabla \times V· dS$, where
\[V (x, y, z) = xy^2 z\hat{i} − 4x^2y\hat{j} + \frac{z-1}{x^2+2y^2+1}\hat{k}.\]


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Erdos Erdos
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