Answer to Question #275266 in Math for v-sshi

Question

Let S be the closed parabolic bowl consisting of two pieces: S1: z = x2 + y2

, x2 + y2 ≤ 1;

and S2: x = rCos(ɸ), y = rSin(ɸ), z = 1 for 0≤ɸ≤2π, and 0≤r≤1. Let (the vector)

F = (x-y+z)î + 2xĵ + k̂

. Compute both sides of Gauss’s Divergence Formula and show that they are equal.