a) Compute the Jacobian of the change of variables from spherical coordinates to rectangular coordinates. b) Assuming
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b) Assuming that Vol is translation and rotation invariant (see Exercises 12.1.7 and 12.4.7), verify the following classical formulas: the volume of a sphere of radius r is 3/4πr3, and the volume of a right circular cone of altitude h and radius r is πr2h/3.
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a Let Then b Since Vol is translation and rotation invariant we can compute the volume of a typica...View the full answer
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