Question

Given F = xi - yj, find the value of ∬Fn dS over the closed surface bounded by the planes z = 0, z = 1, and the cylinder x2 + y2 = a2, where n is the unit outward normal, by direct calculation. (Hint: The element of area is dS = a dθ dz in cylindrical coordinates on the curved surface.)

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Integral Calculus

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