Calculus BL94

1
Calculus B L94 Solids of Revolution
IV Displaced Axes of Revolution
Disk/Washer Method
If the axis of revolution is parallel to
the x-axis, the variable of integration is x.
If the axis of revolution is parallel to
the y-axis, the variable of integration is y.
Shell Method
Vise-versa
2
Ex1. The region R is bounded by the x-axis, y
x3, and x 1. Find the volume of the solid
formed when R is revolved about the line x 1.
Disk method
dy
r

3
Ex2. The region R is bounded by x y2 1, and
x 2. Find the volume of the solid formed when
R is revolved about the line x 3.
Washer method
R
dy
r

4
Ex3. The region R is bounded by the y ex, x
2, x 3, and y 0. Find the volume of the
solid formed when R is revolved about the line
x 4.
Shell method
r
h

dx