The volume of , found in Example 8.1.14, is given by
=
Table 8.3.4(a) lists the first moments and the coordinates of the centroid.
First Moments
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Centroid
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Table 8.3.4(a) First moments and the coordinates of the centroid
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When the region supports the density , the total mass in is
=
Table 8.3.4(b) lists the first moments and the coordinates of the center of mass under this condition.
First Moments
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Center of Mass
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=
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=
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=
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=
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=
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=
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Table 8.3.4(b) First moments and the coordinates of the center of mass
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In each integral, the Jacobian must be inserted, and where applicable, the "lever arms" are replaced respectively by , , and .