Find the exact coordinates of the centroid for the region bounded by the curves $y=\frac 1x$, $y=x$, $y=0$ and $x=2$

Question

Im not sure how to set up these integrals. I tried using $y=x$ as the upper curve and subtract $y=\frac 1x$ in my integrals but I still am not getting the correct answer. If anyone knows how to do this and could help me out it would be greatly appreciated. Thanks!