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Homework Help: Volume calculation

  1. Jan 19, 2012 #1

    Find the volume of the solid:

    y = 2 - x/2 bounded by y = 0, x = 1, x = 2.

    Answer: 19pi/12.... I already know how to get the answer but....

    what if wanted to use horizontal rec? For instance If I am using the vertical rec... the radius would be y = 2 - x/2... but if I use the horizontal rec would the radius be x = 2(2 - y) ? I tryed this value and integrated from y = 0 to y = 3/2... but did not get the correct answer....

    Is it not possible to get the correct answer using horiz. rec?

    Attached Files:

  2. jcsd
  3. Jan 19, 2012 #2


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    Staff Emeritus
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    Are you rotating this trapezoid around the x-axis to form the solid of revolution?

    If so, then integrating w.r.t x is the disk method.

    Integrating w.r.t. y is the shell method (cylindrical shells), so the radius is y itself. You will have to break the integration up into sum of two integrals.
  4. Jan 20, 2012 #3
    Yes I am rotating across the x-axis. So is it possible to use horizontal rec?
    Last edited: Jan 20, 2012
  5. Jan 20, 2012 #4
    Where can I learn about the shell and disk method? My teacher didnt mention these techniques.
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