Recall that the y-value of the center of mass is given by
y ¯ = ∬ R y ρ ( x , y ) d A ∬ R ρ ( x , y ) d A {\displaystyle \displaystyle {\overline {y}}={\frac {\iint _{R}y\rho (x,y)\;{\text{d}}A}{\iint _{R}\rho (x,y)\;{\text{d}}A}}}
