# Dedicated to great Mark Hennings

Calculus Level 5

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

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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