Use the Divergence Theorem to calculate the surface integral 

F · dS;

 that is, calculate the flux of F across S.

F(x, y, z) = x4i − x3z2j + 4xy2zk,

S is the surface of the solid bounded by the cylinder 
x2 + y2 = 4
 and the planes 
z = x + 3 and z = 0.

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