The triangle whose coordinates of the center of mass You have to compute is illustrated in the figure...

The computation is performed in two steps...

a) first computing the mass m of the triangle...

(1)

b) then computing the coordinates of the center of mass...

(2)

For the function we can set k=1 so that is and the integral (1) becomes...

(3)

... and integrals (2)...

(4)

Kind regards