$\"\"$

The equation of the parabolic spandrel is $\"\"$ .

Shaded region is bounded by the graphs $\"\"$ and $\"\"$ .

Consider $\"\"$ , $\"\"$ on $\"\"$ .

Area of the region is $\"\"$ .

$\"\"$

$\"\"$ .

Coordinates of center of mass $\"\"$ are $\"\"$ and

$\"\"$ .

$\"\"$

$\"\"$ .

$\"\"$

The center of mass is $\"\"$ .

$\"\"$

The center of mass is $\"\"$ .