A-Level Further Core 1

Volume of Revolution

In regular integration of a function you obtain the area under by considering smaller rectangles with height and width so the approximate area is as this is written as

For a Volume of Revolution you do the same however the areas are small cylindrical volumes. These volume is in this case is the radius and we consider (the width in the case) going to zero so the approximate area as . The exact volume is written as

You can do the same thing for a volume of revolution around the y axis by rearranging to get then the volume will be

Keep in mind that and are values of and that the radius of the volume is from the axis going across parallel to the axis until the curve.


A-Level Further Core 2

Volume of Parametric Revolution

For a parametric equation defined you can find the volumes of revolution with the following formulae:

About the x axis

About the y axis