Let the segment taken at some arbitrary distance x from the origin (where x lies in the interval [-2,2]) have volume δV and thickness δx.
By Simpson's law:
δV=(8/3)y^2*δx (note it is only approximately equal to this expression)
V=sum from x=-2 to x=2 of [(8/3)y^2 * δx]
However, this is only an...