Final answer:
The mass of a lamina can be found by integrating the density function over the area defined by the lamina's vertices. A double integral is used if the density function varies within the region. Without specific vertices or a density function, we cannot provide an exact calculation.
Step-by-step explanation:
To find the mass of a lamina with given vertices and density function, we typically integrate the density function over the area of the lamina. If a lamina has a two-dimensional shape bounded by vertices and the density function varies through the shape, you apply a double integral over the region defined by these vertices. The density function would be given as ρ(x, y), where ρ represents the mass per unit area at any point (x, y) on the lamina.
Since no specific vertices or functions are provided in the information given, we would need that information to proceed with an actual calculation. Additionally, when dealing with variable density, such as a linear or quadratic function, we would integrate the density function multiplied by a differential area element over the entire region of the lamina.
For example, if the density was given by a quadratic function ρ(x) = ρ0 + (ρ1 − ρ0) (±) ² along a rod of length L on the x-axis, you would integrate from 0 to L to find the total mass.