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Vector Fields and Surface Integrals

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Find the flux of the vector field F(x, y, z) = (y, 0, z2) out of the unit sphere S. In other words, find the surface
integral ∫∫S (y, 0, z2) * dS, where the sphere S is oriented by the outward normal.
Let S be the cylinder x2 + y2 = 1, 0 ≤ z ≤ 6. Find ∫∫S (x4 + 2x2y2 + y4)2 dS.

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Vector fields and surface integrals are investigated. The solution is detailed and well presented.

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