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Homework Help: Cylindrical Shells

  1. Sep 12, 2006 #1
    Use cylindrical shells to calculate the volume of the solid obtained by rotating the region bounded by y=x and y=x^2-2x about the line y=3
    I know how do set the problem up and how to do it, I just don't know how to write "y=x^2-2x" in terms of "x". This is how I think the problem should be set up, with the changes made to the equation so everything in the equation will be "y's" or "dy's".

    integrate from -1 to 0 : 2pi y (x^2-2x) dy + integrate from 0 to 3: 2pi y {y-(x^2-2x)} dy
    Last edited: Sep 12, 2006
  2. jcsd
  3. Sep 12, 2006 #2


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    Staff: Mentor

    Welcome to PF, nobli. We are happy to be of help, but you must show us your work to start things off. Have you made a sketch of the volume? What coordinate system would probably be the easiest to use for this integration? What is the form of the dV vector in that coordinate system?

    EDIT -- fixed a typo
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