1. The problem statement, all variables and given/known data A solid metal rod with dimensions 5 x 2 x 1 is placed with one corner at the origin, such that 0≤x≤5, 0≤y≤2 and 0≤z≤1. The rods density is described by ρ(x) = (3x2 +10x) / 25 a) find the total mass of the rod b) find the x-coordinate of the centre of mass of the rod. 2. Relevant equations Total mass, M = ∫ dm = ∫ ρ dV X coordinate of COM = (1/M) * ∫xdm = (1/M) * ∫xρ dx 3. The attempt at a solution a) By substituting the density function into the Total mass integral and doing a triple integral over dxdydx, i get: M = ∫∫∫ (3x2 +10x) / 25 dx dy dz = ∫∫ [(x3 +5x2) / 25] dy dz with limit of 5 and 0. From there I continue and get an answer of M = 20 units My problem arises in part b) when I do: (1/M) * ∫xdm = (1/M) * ∫xρ dx = (1/M) * ∫ (3x3 +10x2) / 25 dx and use the limts of 5 and 0, i arrive at an X-coordinate for the centre of mass as 1.77. This doesnt make sense to me as surely with the stated denisty function, the mass if increasing as you progress from x=0, resulting in the COM being shifted towards the x=5 end? Any help would be appreciated !