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Homework Help: Integration Volume

  1. Sep 29, 2007 #1
    there are the two types of volume integration which i am aware of, disc-integration and shell integration. What is the difference between these? where would each one? Also i was looking at shell integration on carious sites on the net, and i am still a little confused how the generic formula works. Could someone ever so kindly explain this to me?

    many thanks,
  2. jcsd
  3. Sep 29, 2007 #2


    Staff: Mentor

    The difference between disk and shell integration is where the axis of rotation is. Lets assume that you are integrating a solid of rotation of some f(x)dx. If the axis of rotation is parallel to the x axis then you use disk integration, but if the axis of rotation is perpendicular to the x axis then you use shell integration.
  4. Sep 29, 2007 #3
    How would you find the general vector equation of a solid of revolution?
  5. Sep 29, 2007 #4


    User Avatar
    Science Advisor

    "Disks" works, of course, by using disks- normally, the radius of the disk is the value of the function and you calculate the area by [itex]\pi f(x)[/itex], multiply by the "thickness", dx, and then integrate.

    "Shells" works by using thin cylinders. The radius is typically the x-value so you have a "circumference" calculation [itex]2\pi x[/itex] and then multiply by the "height" of the cylinder, f(x): you integrate [itex]2\pi x f(x) dx[/itex\.
  6. Sep 29, 2007 #5
    okay thanks for the replies
    it is a little less confusing now
    ill try reading into in more and repost if i am still stuck,
    thanks once again for your time,
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