(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am trying to sort out surface integrals in my head, and have become more confused when attempting to calculate the surface integral of a hemisphere. I am getting confused about which values to use as boundaries.

2. Relevant equations

da=R^2 sinθdθdφ

3. The attempt at a solution

To get half a sphere I integrated dφ between 0 and 2pi, and integrated sinθdθ between 0 and pi/2.

This gives R^2*0*2pi=0

Whereas if I integrate dφ between 0 and pi, and integrate sinθdθ between 0 and pi i get

R^2*1*pi

which is the answer I am looking for but shouldn't I get the same using both sets of boundary values? Confused...

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# Homework Help: Surface integral of half sphere

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