1. The problem statement, all variables and given/known data Let a rod with length L and constant cross-sectional area A have the density ρ(x) = ρ((3.x^2 + 2.x.L)/L^2) 0 ≤ x ≤ L where x is the distance from one end of the rod and ρ0 is a real constant. (a) Find the total mass M of the rod. (b) Find the x-coordinate xc of the centre of mass of the rod. (c) Find, in terms of M, the moment of inertia of the rod about the vertical axis through x = 0. 2. Relevant equations M = ∫Aρ(x).dx 3. The attempt at a solution M = ∫Aρ(x).dx M= A.ρ∫((3.x^2 + 2.x.L)/L^2).dx I am slightly confused where to go from here! Do I use integration by parts?