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Find volume between parabloid and parabolic sylinder

  1. Mar 4, 2012 #1
    EDIT - well its too late to change the title now, but I can spell corectly... sometimes.

    1. The problem statement, all variables and given/known data
    Find the volume of the region bounded by x = y**2 and z**2 and x = 2 - y**2


    2. Relevant equations
    Triple integrals and cylindricals


    3. The attempt at a solution
    I started by roughly graphing the two figures and I got stuck here for some reason. I tried cylindricals, but I figured there would be a better way. For whatever reason I can't get my head around the limits of integration for this problem. Solving the integral once I have it shouldn't be a problem, but I just need to setup the integral thats why my work here is limited. Thanks for any help
     
  2. jcsd
  3. Mar 4, 2012 #2

    tiny-tim

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    Hi MeMoses! :smile:
    I think you meant a diabolic sylinder! :biggrin:
    One surface is of revolution, but the other isn't, so there's no short-cuts here. :redface:

    You'll have to take slices of width dx perpendicular to the x-axis, and then slice those slices either "horizontally" (with width dz) or "vertically" (with width dy), and double-integrate :wink:
     
  4. Mar 4, 2012 #3

    The real question is...
    What's a Sylinder?
     
  5. Mar 4, 2012 #4

    LCKurtz

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    What does the red highlighted definition mean? There isn't an equation after the word "and".
     
  6. Mar 4, 2012 #5

    tiny-tim

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    Hi LCKurtz! :smile:

    "and" means "+" :wink:
     
  7. Mar 4, 2012 #6

    LCKurtz

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    How do you know he doesn't mean ##x = y^2## and ##x = z^2##?
     
  8. Mar 4, 2012 #7

    tiny-tim

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    the title? :rolleyes:
     
  9. Mar 4, 2012 #8

    LCKurtz

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    Well, given that he obviously didn't post the problem word for word, I wouldn't make the assumption that the title is correct. Perhaps the problem is actually stated as I propose and the OP thinks that makes a paraboloid. No way of knowing until we see the correct wording one way or the other.
     
  10. Mar 4, 2012 #9
    My bad, its x = y**2 + z**2 as thought
     
  11. Mar 4, 2012 #10
    Would the limits
    y**2+z**2 < x < 2-y**2,
    -sqrt(1-(z**2)/2) < y <sqrt(1-(z**2)/2),
    -sqrt(2) < z < sqrt(2)
    get the correct volume?
     
  12. Mar 4, 2012 #11

    LCKurtz

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    Yes, those are correct.
     
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