I am to derive the volume of a sphere using spherical coordinates. I have derived the (correct) jacobian as r^2sin(theta) dr d(theta) d(phi) so its simply a matter of integrating over the correct limits.
What I don't get is why we use 2pi to 0 for phi and pi to 0 for theta, when surely the definition of spherical coordinates uses the opposite limits for the two coordinates.
The Attempt at a Solution
Here http://en.wikipedia.org/wiki/Multiple_integral#Example_of_mathematical_applications_-_Calculations_of_volume" the correct formula is derived using these limits, so I know it works. But why?
Any help appreciated!
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