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PAGE: 541SET: ExercisesPROBLEM: 65
Please look in your text book for this problem Statement

The graphs of the inequalities are , ,  and .

Graph the inequalities , ,  and .

Observe the graph :

 on .

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.

Find the area of the region .

Substitute .

Apply derivative on each side with respect to .

.

Substitute  and .

Substitute  and .

The area of the region is .

Find .

.

Find .

Since the graph is symmetrical about the -axis, center of mass lies on the axis of symmetry.

The center of mass  is  and .

Substitute  and  in .

.

Substitute  and  in .

.

The centroid of the region is .

The centroid of the region is .



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