Multivariable Calculus: Cylindrical and Spherical Coordinates, Problem 5

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A triple integral is converted from rectangular coordinates to spherical coordinates and cylindrical coordinates. Also a discussion of how symmetry shows the integral evaluates to 0 without needing to do any calculations.
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Why don't you calculate the r in the cylindrical coordinates like how you did p in spherical coordinates? Don't they both represent the radius?

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