The equations are , .

Moments and center of mass of a planar lamina:

Let  and  be continuous functions such that   on , and consider the planar lamina of uniform density  bounded by the graphs of  and .

The moments about the -and -axes are

.

.

The center of mass  is  and , where  is the mass of the lamina.

Graph the equations , .

Shade the region bounded between the equations.

Observe the graph:

The area of the region is .

.

Find .

Consider ,  on  in .

.

Graph the function  on interval .

Observe the graph:

.

.

Find .

Substitute ,  on  in .

Observe the graph:

.

.

Since the center of mass lies on the axis of symmetry, .

Substitute  and  in .

.

Substitute  and  in .

.

The center of mass is .

The center of mass is .