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Polar and spherical coordinates seem very useful for areas, however I don't understand why I can't seem to keep a direction after a spherical integral. In Cartesian coordinates, it's very easy to integrate component by component and end up with a vector, but is it possible to do the same in polar/spherical?

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  • $\begingroup$ It depends on the question. For me, polar is much easier than spherical. $\endgroup$
    – usukidoll
    Feb 7, 2014 at 8:17

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Can "keep a direction" if you understand the underlying idea. See the formulas at http://plaza.obu.edu/corneliusk/mp/suv.pdf.

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