I have a function f(r, [tex]\phi[/tex], [tex]\vartheta[/tex]) = 3cos[tex]\vartheta[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

Evaluating the repeated integral of this function over the surface of a sphere, centered at the origin, with radius 5, I have come up with 0 as my result. I'm not sure if this is correct. I've double checked my calculations, and tried subdividing the surface S into smaller subsections and summing the integrals of each section, and I get the same result. Intuitively it makes some sense that the answer would be 0 since cos[tex]\var{theta}[/tex] takes on values either side of 0 for [tex]\vartheta[/tex] in the intervals [0, pi] and [pi, 2pi].

Still, for some reason I'm uncomfortable with this result. Can anybody shed some light on this?

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# Integral of f over the surface of a sphere (in spherical polar coordinates)

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