What i've tried:Find the centroid of the rectangular region cut from from the first quadrant by the line .
This means that the centre of mass is .
However, intuitively this doesn't seem right to me. I would expect it to be at since that would be the middle of the two sides (and the expression for the density is constant).
So can anyone see if is correct. If it isn't correct, where have I gone wrong in my integrals?