High school students in a physics class are asked to measure the mass of a non-homogeneous rod where the density varies along its length.

What is known:

• The density of the rod can be modeled as
        ρ(x) = x² - x + 3
  where x is the length. The density function, ρ(x), has units of g/m.
• The length of the rod is 4 m.

Determine the mass of the rod.

• If the rod is divided into many small pieces, the total mass of the stick can be approximated by summing the mass of each piece.
  
       
  
• The definite integral can be used if the number pieces became infinite