2-24b Divergence Theorem - Nested Spheres

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

[redSTEM]

!! final solution works out to -pi/3 but there are two important errors in this problem,
please click on the pdf solution to see the fixes, errors 1 & 2 described below
1. the bounds are switched for dR ( should be 3 top 2 bottom)
2. the partial derivative of d/dR(1/R) from the del operator dot A is equal to -1/R^2 the problem drops the negative and has it as -1/R^2.
solution works out to -pi/3