Question involving the Divergence Theorem and Surface Integrals

lys04
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Homework Statement
Divergence theorem problem
Relevant Equations
Divergence theorem, surface integrals
Is this correct? Ignore my bad drawings
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It looks fine, but in the future please do not simply post images. The forum has a perfectly functioning LaTeX implementation, use it! If you just post a screenshot of your compiled math there is no possibility for us to quote particular sections of your post and it is less readable.
 
Will do! Thanks
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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