Disc Method Around the y-Axis (College Board AP® Calculus AB)

Volume with disc method revolving around the y-axis

What is a volume of revolution around the y-axis?

• This is very similar to a volume of revolution around the -axis

• A solid of revolution is formed when an area bounded by a function
  (and other boundary equations) is rotated radians around the -axis

• The volume of revolution is the volume of this solid

How can I use the disc method to calculate a volume of revolution around the y-axis?

• For a continuous function , if the region bounded by

  • the curve and the -axis

  • between and

• is rotated radians around the -axis, then the volume of revolution is

  •  

    • Note that here is a function of

      • This will mean rewriting in the form

    • Also note that the integration is done with respect to

• If and are not stated in a question, these boundaries could involve

  • the -axis ()

  • and/or a -intercept of