Question

Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D is the triangular region with vertices (0, 0), (2, 1), (0, 3); rho(x, y) = 4(x + y)

Answer 1

Mass of the lamina is 24

Centre of Mass is
`((3)/(4),(3)/(2))`

Explanation:

(1) the x-bound are 0≤x≤2

the line passing through (0,0) and (2,1) has equation y = x/2

line passing through (0,3) and (2,1) has equation y = -x + 3

so, the y-bound are x/2≤y≤-x +3

Check attachment for further calculations.....