I have to integrate over the northern hemisphere of a sphere. The answer states that the integration bounds for r is 0 to R, for theta it's 0 to pi/2, for phi it's 0 to 2pi. What I don't understand is why theta doesn't go from 0 to 2pi. If I had to set this up, I would have theta going from 0 to 2pi and phi going from 0 to pi. Can someone please explain this.