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In a solid mass of material, the infinitesimal mass [math]dm[/math] of an infinitesimal amount of volume [math]dv[/math] located at an arbitrary point is given by

[[math]] dm = \rho \; dv , [[/math]]

where [math]\rho[/math] is the density of the material at that point. Consider a cylindrical container of radius [math]a[/math] filled to a depth [math]h[/math] with a liquid whose density is greater at the bottom and less at the top. Specifically, at a point a distance [math]x[/math] below the surface the density is given by [math]\rho = 2 + x[/math]. What is the total mass of liquid in the container?