Question: Consider the cylinder \(x^{2}+y^{2}=9,-3 \leq z \leq 3\).

1. Find a parametrization of the surface using \(\theta\) and \(z\). Be sure to include the limits on the variables.
2. Evaluate \(\iint_{S} \mathbf{F} \cdot d \mathbf{S}\), where \(\mathbf{F}(x, y, z)=y \mathbf{i}+x^{2} y \mathbf{j}+e^{x z} \mathbf{k}\).

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