Question

Find the center of mass of a thin plate covering the triangular region cut from the first quadrant by the line
y = -x + 3, with density δ(x) = x.

Answer 1

Take rectangular strips of length dx at a distance x from origin perpendicular to y axis dm becomes
density*V. Find V in terms of x and dx(You know the equation of the line).
Then integrate from 0 to 3. y coordinate is same as that of a normal triangular plate.

Answer 2

find side length and multiply by dx to find V