Use the divergence theorem to calculate the surface integral ? ? s f · ds; that is, calculate the flux of f across s. f(x, y,z = x2y i xy2 j 4xyz k s is the surface of the tetrahedron bounded by the planes x = 0, y = 0, z = 0, and x 5y z = 5.

By the divergence theorem, the surface integral given by



(where the integral is computed over the entire boundary of the surface) is equivalent to the triple integral



where is the volume of the region bounded by .

You have




and so the integral reduces to

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