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Series: Calculus: Disks and Washers


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About this Series

  • Lessons: 5
  • Total Time: 0h 59m
  • Use: Watch Online & Download
  • Access Period: Unlimited
  • Created At: 07/29/2009
  • Last Updated At: 07/20/2010

In this 5-lesson series, we'll learn about the Disk Method and its many applications. The disk method is an integration technique that allows us to calculate the volumes of different disks and washers. Revolving a plane region about a line forms a solid of revolution. You can calculate the volume (V) of a solid of revolution using the disk method where R(x) is the radius of the solid of revolution with respect to x and V equals pi times the integral on the interval [a,b] of R(x)^2dx.

To find the volume of a solid of revolution, you can often divide the region into slices. Each slice resembles a disk, so this method is called the disk method. To find the volume, just integrate the areas of the disks across the given interval. The radius of a given disk is equal to the height of the original region. The area of a disk equals the
area of a circle. Once you find the area, just integrate.

Solids of revolution (and their calculated volumes) can be based off of revolutions around either the x or y axis depending on the function. Additionally, the difference between the volumes of an out and an inner solid of revolution gives us the volume a washer, as washers are disks with smaller disks removed from the center. Just like simple solids of revolution, volumes of washers can be calculated whether they revolve around the x or y axis.

Taught by Professor Edward Burger, this series comes from a comprehensive Calculus course. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers limits, derivatives, implicit differentiation, integration or antidifferentiation, L'Hopital's Rule, functions and their inverses, improper integrals, integral calculus, differential calculus, sequences, series, differential equations, parametric equations, polar coordinates, vector calculus and a variety of other AP Calculus, College Calculus and Calculus II topics.

About this Author

2174 lessons

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Thinkwell lessons feature a star-studded cast of outstanding university professors: Edward Burger (Pre-Algebra through...

Lessons Included

~ greenshoes

great explanation! Thank you!

Below are the descriptions for each of the lessons included in the series:

Supplementary Files: