The center of mass formula:
b
(xM)*M=S xλ(x) dx.
a
This formula can be derived from the physical premise
that, if the rod is broken up into a finite number of
pieces of masses M1,...,Mn and centers of mass xM1,...xMn,
then (xM)*M=(xM1)*M1+...(xMn)*Mn.
Carry out the derivation.
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