If F = x i + y j, calculate the flux of F upward through the part of the surface z = 4 - x² - y² that lies above the (x, y) plane by applying the Divergence Theorem to the volume bounded by the surface and the disk that it cuts out of the (x, y) plane. A) 14 $\pi$ B) 16 $\pi$ C) 18 $\pi$ D) 20 $\pi$ E) 8 $\pi$

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Quizplus · Accepted Answer

The divergence of F is 2. The volume is a paraboloid with height 4 and base radius 2. The volume is (1/2) * base area * height = (1/2) * π * 2^2 * 4 = 8π. The flux is the divergence times the volume, 2 * 8π = 16π.

If F = X I + Y J, Calculate the Flux