The linear density in a rod √3 meters long is (12/(1+x^2)) kg/m, where x is measured in meters from one end of the rod. Find the average density (in kg/m) of the rod.
Average density = ??
total mass is
∫[0,√3] 12/(1+x^2) dx = 12arctan(x) ]0,√3] = 12*π/3 = 4π kg
so the avg density is mass/length = 4π/√3 kg/m