if you have a rod length 5 with density p(x)=2+(x/5), how would you go about finding the center mass of the rod?

Question

any suggestions?

Answer 1

You can think of the center of mass as being the average position of all the particles making up the rod.  An infinitesimal portion of the rod dx has mass dx*(2+x/5) (neglecting its cross-sectional area, which we know nothing about and don't care about anyway) and is at position x.  If you integrate the product of these, and then divide by the total mass (which requires its own integration of the density equation alone), you can get the position of the center of mass.