Spherical polar coordinates triple integral

A triple integral in Cartesian coordinates is transformed into a triple integral in spherical polar coordinates by... 

SOLUTION In spherical polar coordinates, the volume of a sphere with radius R is found from the triple integral ... 

When one performs integrations in spherical polar coordinates, the form of dr and the limits of integration must be considered. The full form of dr for integration over all three coordinates (which would be a triple integral, each integral dealing independently with a single polar coordinate) is... 

Problem. The differential volume element in spherical polar coordinates is 4V = sin 0 d(p d dr. Given that goes from 0 to 2 r, 9 goes from 0 to jr, and r goes from 0 to r, evaluate the triple integral... 

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See also in sourсe #XX -- [ ]

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