Question

A lamina occupies the part of the disk in the first quadrant and the density at each point is given by the function.

a. what is the total mass?
b. what is the moment about the x-axis?
c. what is the moment about the y-axis?

Answer 1

To find the total mass of the lamina occupying the first quadrant of the disk, integrate the density function over the region. The moments about the x-axis and y-axis can be calculated using the formulas mentioned.

Step-by-step explanation:

a. To find the total mass, we need to integrate the density function over the region occupied by the lamina in the first quadrant of the disk. The mass can be calculated by the formula:

m = ∫∫ ρ(x, y) dA

where ρ(x, y) is the density function of the lamina and dA is the differential area. You'll need to provide the specific density function to proceed with the calculation.

b. The moment about the x-axis can be found using the formula:

M_x = ∫∫ y × ρ(x, y) dA

c. The moment about the y-axis can be found using the formula:

M_y = ∫∫ x × ρ(x, y) dA