R

The region R is bounded by the curves $y=2x$, $y=8-x^{2}$, and the y-axis, and its mass density is $\delta (x,y) = xy$. To find the center of gravity of the region you would compute $\displaystyle\int\int_R\delta(x,y)\, dA= \int_c^d\int_{p(x)}^{q(x)}\delta(x,y)\,dy\,dx,\int_c^d\int_{p(x)}^{q(x)}x\delta(x,y)\, dy\,dx,$ and $\displaystyle\int_c^d\int_{p(x)}^{q(x)}y\delta(x,y)\,dy\,dx$ where
$c =$
$d =$
$p(x) =$
$q(x) =$
$\displaystyle\int_c^d\int_{p(x)}^{q(x)}\delta(x,y)\,dy\,dx =$
$\displaystyle\int_c^d\int_{p(x)}^{q(x)}x\delta(x,y)\,dy\,dx =$
$\displaystyle\int_c^d\int_{p(x)}^{q(x)}y\delta(x,y)\,dy\,dx =$
and finally the center of gravity is
$\overline {x} =$
$\overline {y} =$