What is the mass of a sphere of radius a*R where the density at any point distance x*R from the sphere's centre is f(x) where f(x) is an algebraic function of x? R is the radius of a sphere with a common centre to this one but of larger or equal radius and a thus takes a value between 0 & 1. My solution: Consider sphere made up of infinite number of spherical shells. Assume that a spherical shell is at distance x*R from centre with infinitesimal thickness dx. Volume of spherical shell = its surface area * its thickness = 4Pi((x*R)^2) * d(x*R) Mass of spherical shell = mass of spherical shell * density of spherical shell = 4Pi((x*R)^2) * d(x*R) * f(x) = 4Pi(R^3)(x^2)f(x)dx Mass of sphere = Integral from a to 0 of 4Pi(R^3)(x^2)f(x)dx = 4Pi(R^3) * Integral from a to 0 of (x^2)f(x)dx The reason I ask this is that Brian Cox & Jeff Forshaw in the footnote on p235 of their book "The Quantum Universe: everything that can happen does happen" state: g(a) = 4Pi(R^3)p * Integral from a to 0 of (x^2)f(x)dx where g(a) is the fraction of a star's mass lying in a sphere of radius aR (e.g. a=0.5 means that this sphere has half the radius of the star), R is the radius of the spherical star, p is the average density of the star, f(x) is the density of the star at a point distance x*R from the star's centre. My view is that: g(a) = 4Pi(R^3) * Integral from a to 0 of (x^2)f(x)dx / ((4Pi(R^3)/3) * p) = Integral from a to 0 of (x^2)f(x)dx / (1/3) * p) Am I correct in this result? PS apologies for not using the mathematical symbols for Integral, Pi etc: I haven't figured out how to get them into this webpage.