Use the divergence theorem to calculate the surface integral s f · ds ; that is, calculate the flux of f across s. (give your answer correct to at least three decimal places.) f(x, y,z) = x3 i + 2xz2 j + 3y2z k s is the surface of the solid bounded by the paraboloid z = 4 ? x2 ? y2 and the xy-plane

The divergence of the vector field is given by



By the divergence theorem, the integral over the surface is equivalent to the triple integral over the region bounded by (call it ).



The triple integral can be precisely written as



which is easy enough to evaluate directly. You should find that its value is .

The correct graph is the second one, with the points being at (-6,0), (2,0) and reaching down to (-2,-8)