Find the centroid of the area bounded by the curve
$\displaystyle
2y^2+2y-x-2=0
$
and the line $\displaystyle x=2y$.
Do you know how to double integrate?
$\displaystyle x=2y^2+2x-2$
$\displaystyle x=2y$
$\displaystyle \int \int ~dA$
Using $\displaystyle dA = dx~dy$ will be better. It'll be easier to apply the bounds for y, because the functions are y's functions.
A = $\displaystyle \int \int ~dx~dy$
M_x = $\displaystyle \int \int y ~dx~dy$
M_y = $\displaystyle \int \int x ~dx~dy$
$\displaystyle \bar {x} = \frac{M_y}{A}$
$\displaystyle \bar {y} = \frac{M_x}{A}$
And the centroid is $\displaystyle O(\bar {x},\bar {y})$.
Now apply the bounds and integrate and so on..