User:Kevinsam/sandbox

Calculate the volume of a generalized n-dimensional sphere:

First, the surface of a sphere is the set of all points a given distance from the origin in n-space. So, by the distance formula, a sphere of radius r is the set of all points which satisfy the equation

x1sq+x2sq+...+xnsq=rsq

More conveniently for our purposes, we can parameterize the surface like so:

>>>

Justification: