Volumes+of+solids+of+revolution

In order to find the volume of a rotating a solid follow these steps:

1) Determine the axis of rotating

For horizontal axes 2) Determine where the two curves intersect 3) Integrate outer^2-inner^2 fromthe left intersection to to the right intersection.

If the axis is farther than the inner, the graph will have a hole 4) Integrate (Axis-outer)^2- (axis-inner)^2 to find the volume.

For vertical axes 5) Solve the equations for x 6) Integrate outer^2-inner^2 from the bottom intersection to to the top intersection.

If the axis is farther than the inner, the graph will have a hole 7) Integrate (Axis-outer)^2- (axis-inner)^2 to find the volume.

