The total mass of the rod.
If the mass of the rod measured from the left end to a point x is m(x) then, the linear density is ρx=m'(x).
Therefore, mx=∫abρxdx is the total mass of the rod lying between x=a and x=b.
Since ρx=m'(x), the total mass of the rod lies between x=0 and x=4 is
Integrating using rules of integration we have,
The total mass of the rod lyingbetween x=0 and x=4 is 1403 kg
The total mass of the rod is 1403 kg