Volume By Rotation
(Section 6.1)
The volume of a slice is the area of the slice multiplied by the
width of the slice.
V
i
= (area of side of slice
i
)(width
i
).
The total volume is then:
V
A
(
x
)
dx
a
b
or
V
A
(
y
)
dy
c
d
.
We are going to examine slice perpendicular to an axis of
revolution.
When we revolve the slices, we get disks or washers
depending on the initial region.
Always make slices perpendicular to axis of revolution.
Always integrate along the axis perpendicular to a slice.
DEF
The Disk Method
T volume of a solid of revolution whose cross-sections are circular
disks of radius
R(x)
is
V
A
(
x
)
dx
a
b
[
R
(
x
)]
2
dx
a
b

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