Use the Divergence Theorem to find the flux of F = xy²i + x²yj + yk outward through the surface of the region enclosed by the cylinder x² + y² = 1 and the planes z = 1 and z = -1.

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THEOREM 8-Divergence Theorem Let F be a vector field whose compo- nents 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 surface's outward unit normal field n equals the triple integral of the divergence V. F over the region D enclosed by the surface: [₁ F.ndo = Outward flux J V.F dV. Divergence integral (2)