The "center of mass" of region A is given by

\(\displaystyle \overline{x}= \frac{\int\int_A\int x \rho(x,y,z) dxdydz}{\int\int_A\int \rho(x,y,z)dxdydz\(\displaystyle

\(\displaystyle \overline{x}= \frac{\int\int_A\int y \rho(x,y,z) dxdydz}{\int\int_A\int \rho(x,y,z)dxdydz\(\displaystyle

\(\displaystyle \overline{x}= \frac{\int\int_A\int z \rho(x,y,z) dxdydz}{\int\int_A\int \rho(x,y,z)dxdydz\(\displaystyle

where \(\displaystyle \rho(x,y,z)\) is the density function. If the density is constant, you can factor it out of the integrals and then cancel. That is, with constant density you can just ignore it (equivalently take it equal to "1").\)\)\)\)\)\)