Find the centroid of the region bounded by the following curves
Centroid : (___, ___)
I will assume it is a homogenous density.
In that case fist find the mass.
In this case simply the area.
To express the region we need the intersection points between the line and parabola.
The upper curve is,
and lower is .
Thus,
Thus,
.
Now we find the first moments.
Thus,
Thus,
Thus,