- #1

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At the point of:

[tex]\int[/tex]sin[tex]\vartheta[/tex]d[tex]\vartheta[/tex]d[tex]\phi[/tex]

Which is to be integrated over a sphere, when integrating from 0 to pi for [tex]\vartheta[/tex] and then from 0 to 2pi for [tex]\phi[/tex], we get 4pi, which is the answer I'm looking for.

But if I integrate [tex]\vartheta[/tex] from 0 to 2pi first, then [tex]\phi[/tex] from 0 to pi, I get 0, which is definitely not the answer I'm looking for.

Can someone tell me why this is? And how I know which to integrate over pi and which to integrate over 2pi generally?