Question

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

Answer 1

The mass of the lamina is given by


`\displaystyle\iint_Df(x,y)\,\mathrm dA=\int_(x=0)^(x=2)\int_(y=x/2)^(y=3-x)3(x+y)\,\mathrm dy\,\mathrm dx=18`