2-24a Divergence Theorem Nested Spheres

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P.2-23 For a vector function A= a=:::.
a) find pA·ds over the surface of a hemispherical region that is the top half of a sphere of radius 3 centered at the origin with its flat base coinciding with the xy-plane,
b) V ·A, and
c) verify the divergence theorem.
PROBLEM ATTRIBUTION: Fundamentals of Electromagnetics, Cheng

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Just a note to answer a question: You can model one sph dS as positive and one as -dS and add them and it becomes outer radius minus inner, just make sure you don't model inner as negative and also subtract Rout-Rin. However if you do 1 +dS and subtracted Rout-Rin the math is also ok. Just don't confuse it and do both!

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