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 -axis are

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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 .

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Find .

Consider , on in .

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Graph the function on interval .

Observe the graph: 

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Find .

Substitute , on in .

Observe the graph:

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

Substitute and in .

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Substitute and in .

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The center of mass is .

The center of mass is .