9.6 Exercise 11

Find the center of mass of a rod of length L whose mass density changes from one end to the other quadratically. That is, if the rod is laid out along the x-axis with one end at the origin and the other end at $x = L$, the density is given by $\rho \left(x\right) = \rho_{0} + \left(\rho_{1} - \rho_{0}\right) \left(\frac{x}{L}\right)^{2}$, where $\rho_{0}$ and $\rho_{1}$ are constant values.