\[\int \int_{S}(-3xz^{2}\mathbf{i}+z^{3}\mathbf{k}).d\mathbf{A}\]

Let \(S\) be the surface , defined by , \(z=x^{2}+y^{2}\) for \(z\leq 4\).

Then evaluate the double integral above.

Where \(d\mathbf{A}\) is upward-pointing normal vector.

The answer is of the form \(A\pi\) , submit the answer as \(\sqrt{A}\)

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