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Vector Calculus: Flux and divergence theorem

1. Consider a cube with vertices at A=(0,0,0) B=(2,0,0) C=(2,2,0) D=(0,2,0) E=(0,0,2) F=(2,0,2) G=(2,2,2) H=(0,2,2)

A)Calculate the flux of the vector field**F**=x**i** through each face of the cube by taking the normal vectors pointing outwards.

B)Verify Gauss's divergence theorem for the cube and the vector field **F** by computing each side of the formula.

C)Using Gauss's divergence theorem evaluate the flux $\displaystyle \int \int F.dS $ of the vector field **F**=x**i**+y**j**+$\displaystyle z^2$**k** where S is a closed surface consisting of the cylinder$\displaystyle x^2 + y^2 = a^2$, 0<z<b and the circular disks $\displaystyle x^2 + y^2 , a^2$ at z=0 and $\displaystyle x^2 + y^2 = a^2$ at z=b.

I have the basics but dont know how to get an answer. My workings are attatched.