Total Mass of an Interval
The mass of a one-dimensional object is calculated by integrating its density function over the interval of the domain that it occupies.
For a density function ρ(x) of one variables and an object in the domain of ρ occupying a region R, the mass is
The "Density: rho(x)" window shows the density as a color gradient, where cyan indicates rho=0, yellow rho=1, and red rho=2.
The "Mass" window illustrates the mass of the object as the area underneath the function graph of the density function rho.
ExercisesFind the mass of the interval 0 ≤ x ≤ 1 for the density function ρ(x) = x3.
What is a reasonable constraint on the range of the function ρ(x)?