**3. (15 pts)** Recall the definition of moment of inertia for a continuous mass distribution: \[ I = \int r^2 \, dm \] Consider a rod of length \(L\) with nonuniform one-dimensional mass density. If the rod is laid out along the \(x\)-axis with one end at the origin and the other end at \(x = L\), then the density is given by: \[ \rho(x) = \frac{x}{L} \] Find the rod’s moment of inertia about the \(y\)-axis (i.e. about its own end). State your final answer in terms of total mass \(M\) and length \(L\).