The equations are , , and .
Find the volume of the region about the -axis.
The volume of the solid is .
Substitute , and .
.
The equations are , , and .
Shell method:
Vertical axis of revolution.
The volume of the solid is .
The distance from the center of the rectangle to the axis of revolution is .
The height of the rectangle is .
Substitute , and and in .
.
Solve for , when .
Substitute and .
or
.
Therefore , the value of .
The value of .
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