The volume of , found in Example 8.1.5, is given by
=
Table 8.3.2(a) lists the first moments and the coordinates of the centroid.
First Moments
|
Centroid
|
= 0
|
|
=
|
|
=
|
=
|
Table 8.3.2(a) First moments and the coordinates of the centroid
|
|
|
When the region supports the density , the total mass in is
=
Table 8.3.2(b) lists the first moments and the coordinates of the center of mass under this condition.
First Moments
|
Center of Mass
|
= =
|
=
|
= =
|
=
|
= =
|
=
|
Table 8.3.2(b) First moments and the coordinates of the center of mass
|
|
|
In each integral, the Jacobian must be inserted, and where applicable, the "lever arms" and are replaced respectively by , .