Eroxl's Notes
Shell Integration

Disc integration is a method of finding the volume of a solid of revolution by integrating along an axis perpendicular to the axis of revolution, this is in contrast to disc integration and washer integration which both integrate parallel to the axis of revolution.

Function of

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

If

If

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

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.

If

If

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