6. Show that the center of mass of a thin rod of total mass M and length L, whose mass density changes from one end to the other linearly, where

(x) = a+ B (†), where a and B are constant values, is x_{c m}=\frac{L}{3}\left(\frac{3 \alpha+2 \beta}{2 \alpha+\beta}\right) .[3 \mathrm{pt}]