Find center of mass of the lamina that occupies the region D and has the given density function ρ.

Question

D is the triangular region with vertices (0, 0), (2, 1), (0, 3); ρ(x, y) = 5(x + y)

mass=30

Find center of mass

Answer 1

If you found the mass, you're halfway there.

M = ∫ ρ(x,y) dA

The x-coordinate of the center of mass is just

Mx = ∫xρ(x,y) dA / M

and similarly for My.