# This question concerns the vector field F = &minus;xy2

This question concerns the vector fieldF = −xy2 i − x2y j + z(x2 + y2) k.(a) Calculate the divergence of F. Use the divergence theorem to show thatthe flux of F over any closed surface is equal to zero. (b) A cylinder of height h and radius R has its base in the xy-plane and itsaxis of symmetry along the z-axis, as shown in the diagram below.Calculate the flux of F over the curved portion S of the surface of thecylinder by using the result of part (a) to relate the flux of F over S tothe flux of F over the flat top surface T and the flux of F over the flatbottom surface B.
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