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 -axes are .

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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 .