The linear density at any point, x, along the rod is: L = (4-3)/(12-0)x + 3 = 1/12x + 3

Mass = INT L dx = INT{0,12} 1/12x + 3 dx = [1/24x^2 + 3x] from {0,12} = 6 + 36 = 42

I'll have to think about the center of mass for a moment. I don't yet remember how to find this.