density

Mass per unit area at a point, $\rho(x,y)$ , whose integral over a region gives total mass.

Density $\rho(x,y)$ is a local rate — mass per unit area at a point — the same way velocity is a local rate of position. Multiplying $\rho$ by a tiny patch's area gives that patch's mass, exactly the way multiplying a nearly-constant rate by a tiny time interval gives distance; summing those patch masses, refined to a limit, is the mass integral $m=\iint_R\rho\,dA$ .

Examples

A square plate $[0,1]\times[0,1]$ with density $\rho(x,y)=x+y$ has total mass $1$ kg.