TITLE: Need help solving a surface integral question
QUESTION [2 upvotes]: The question is:

I understand the method used in the book. However, when I try a slightly different method, I end up with an incorrect answer: 2$\pi$ instead of 4$\pi$ as given in the book.

I have already tried looking for what I could be going wrong but no avail. Hence decided to ask here.
Thanks in advance.

REPLY [0 votes]: When you wrote out an expression for $dS$, it appears that you're only integrating over the top half of the sphere.
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