![]() We now extend this concept to find the mass of a two-dimensional disk of radius r. If the density of the rod is given by ρ ( x ) = 2 x 2 + 3, ρ ( x ) = 2 x 2 + 3, what is the mass of the rod? Note that although we depict the rod with some thickness in the figures, for mathematical purposes we assume the rod is thin enough to be treated as a one-dimensional object.Ĭonsider a thin rod oriented on the x-axis over the interval. Orient the rod so it aligns with the x -axis, x -axis, with the left end of the rod at x = a x = a and the right end of the rod at x = b x = b ( Figure 6.48). We can use integration to develop a formula for calculating mass based on a density function. ![]() We then turn our attention to work, and close the section with a study of hydrostatic force. Let’s begin with a look at calculating mass from a density function. In this section, we examine some physical applications of integration.
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