Q:  What is the contribution of this little piece
          to the equation for center of mass?

        (mass) * (position)   =  (lambda dx) * (x)


                              =  ( a  +  b x ) (dx) * (x)

        
                                                 2
                              =    a x dx  +  b x  dx
                          



  Q:  What is the location of the center
        of mass of the ruler in the horizontal direction?


               integral over all pieces (  lambda * x dx  )
   X com  =   ----------------------------------------------------------
                         total mass


                               /                  2
                           int |    a x dx  +  b x  dx
                               /
   X com  =   ----------------------------------------------------------
                               /
                           int |   a dx  +  b x dx
                               /



                        (    1     2      1     3  ) x=L
                        (   --- a x   +  --- b x   )
                        (    2            3        ) x=0
   X com  =   ----------------------------------------------------------
                                     1     2    
                            a L  +  --- b L     
                                     2          



                             1     2      1     3        
                            --- a L   +  --- b L         
                             2            3                
   X com  =   ----------------------------------------------------------
                                     1     2    
                            a L  +  --- b L     
                                     2