# Use the Divergence Theorem to find the flux of F = xy^2i + x^2yj + yk outward through the surface of the region enclosed by the cylinder x^2 + y^2 = 1 and the planes z = 1 and z =-1.

Use the Divergence Theorem to find the flux of $F=x{y}^{2}i+{x}^{2}yj+yk$ outward through the surface of the region enclosed by the cylinder ${x}^{2}+{y}^{2}=1$ and the planes z = 1 and z =-1.
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Step 1
Divergence Theorem.
Let F be a vector field whose components have continuous first partial derivatives and let S be a piecewise smooth oriented closed surface. The flux of F across S in the direction of the surfaces