Washer integration, is a method of finding the volume of a solid of revolution by integrating the volumes of many hollow cylinders parallel to the axis of rotation.

Function of

If the line that the function is being rotated around is horizontal line (ie. ) then the following equation can be used to calculate the volume of the solid of revolution.

Where is the start of the solid, is the end of the solid, is the function that is being rotated farthest from the axis of rotation, is the function that is being rotated closest to the axis of rotation, and is the horizontal line (ie. if the axis of rotation is then ).

Examples

TODO

Function of

If the line that the function is being rotated around is vertical line (ie. ) then the following equation can be used to calculate the volume of the solid of revolution.

Where is the start of the solid, is the end of the solid, is the function that is being rotated farthest from the axis of rotation, is the function that is being rotated closest to the axis of rotation, and is the vertical line (ie. if the axis of rotation is then ).

Examples

TODO