A solid region R, whose boundary contains the surface in the figure, is bounded by $z=2y^{2}, z=3,x=0,$ and $x=3$. To find the centroid of R you would compute $\displaystyle\int\int_R\delta(x,y) \,dV= \int_a^b\int_{c}^{d}\int_e^f dz\,dy\,dx, \int_a^b\int_{c}^{d}\int_e^f x\,dz\,dy\,dx,\int_a^b\int_{c}^{d}\int_e^f y\,dz\,dy\,dx$ and $\displaystyle\int_a^b\int_{c}^{d}\int_e^f z\,dz\,dy\,dx$ where
$a =$
$b =$
$c =$
$d =$
$e =$
$f =$
$\displaystyle\int_a^b\int_{c}^{d}\int_e^f dz\,dy\,dx =$
$\displaystyle\int_a^b\int_{c}^{d}\int_e^f x\,dz\,dy\,dx =$
$\displaystyle\int_a^b\int_{c}^{d}\int_e^f y\,dz\,dy\,dx =$
$\displaystyle\int_a^b\int_{c}^{d}\int_e^f z\,dz\,dy\,dx =$
and finally the centroid is
$\overline {x} =$
$\overline {y} =$
$\overline {z} =$