Answer:
[tex]m = \int\limits^a_b \rho(x) \, dx[/tex]
Step-by-step explanation:
The linear density is given by[tex]\dfrac{dm}{dx}[/tex].
[tex]\rho(x) = \dfrac{dm}{dx}[/tex]
[tex]dm = \rho(x)\,dx[/tex]
Integraring both sides to get the mass,
[tex]m = \int\!\rho(x) \, dx + C[/tex]
C is the constant of integration.
With x between a and b,
[tex]m = \int\limits^a_b \rho(x) \, dx[/tex]
