The graphs of the inequalities are , and .

Graph the inequalities , and .

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 ..

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

Find the area of the region .

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From the graph: is area of a quarter circle with radius .

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From the graph: The center of mass is and .

Find .

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Find .

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Find .

Substitute .

Apply derivative on each side with respect to .

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Substitute and .

If then .

If then .

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Find .

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The center of mass is and .

Substitute ,  and in .

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Substitute ,  and in .

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The centroid of the region is .

The centroid of the region is .