Find the centroid $(\bar x,\bar y)$ of the region that is contained in the right-half plane $\lbrace (x,y) \; \vert \; x\geq 0 \rbrace$, and is bounded by the curves: $$y = 3 x^2 + 6 x, \ \ \ y = 0 , \ \ \ x = 0, \ \ \ \mbox{and} \ \ \ x = 2 .$$
$\bar x$=
$\bar y$=