The test question was... We are given a region bounded by the functions √x and x. We were also given the density and mass of the region and asked to only the component y of the centroid. I did not know how to implement these given variables, density and mass into my equation for y bar so I found y bar by integrating the moment about x over total mass. Is my reasoning valid.... the y component of the centroid of the bounded region does not depend on the value of rho or mass given because if density is dispersed evenly through out the region (which it is or atleast it should be from what the book says) then y bar will be at the same location always. The only time it would move is if the density or mass was shifted.