Theorem.
Let
f
be a function which is continuous on the closed interval
[a, b]
. The volume of the solid obtained by rotating the graph of
f
from
x = a
to
x = b
about the
y
-axis is the integral
Discussion using a specific example.
[
Using Flash
] [
Using Java
]
Animation showing the cylindrical shells for the previous example.
[
Using Flash
] [
Using Java
]
Graph of the solid obtained in the previous example.