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Homework Help: Paraboloid problem help

  1. Jul 5, 2010 #1
    1. The problem statement, all variables and given/known data
    The solid enclosed by the paraboloid x=y2+z2 and the plane x=16.


    2. Relevant equations
    Triple integral in ractangular coordinates


    3. The attempt at a solution
    I figured out this is a paraboloid that circles the x axis, that starts at the origin and it gets wider and wider as it goes in the x direction until it is stopped by the plane x=16 where there is a circle around the x axis with a radius of

    [tex]\int_{x=y2+z2}^{16}\int_{z=-\sqrt{16-y2}}^{\sqrt{16-y2}}\int_{z=0}^4 dxdzdy [/tex]

    I was just curious if my set up looks right.

    Thank you.
     
    Last edited: Jul 5, 2010
  2. jcsd
  3. Jul 5, 2010 #2
    Re: Paraboloid

    ok that is not what I meant to write lol, I have to work on this really quick
     
  4. Jul 5, 2010 #3
    Re: Paraboloid

    ok I got what I want up there except for some reason when I try and square stuff, the coding keeps appearing for the stuff in the integrals but not in the first sentence I wrote.
     
  5. Jul 5, 2010 #4

    vela

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    Re: Paraboloid

    In TeX, you use ^ to get a superscript and _ to get a subscript, so x2 would be written x^2 and xmin would be written x_{min}, for example.
     
  6. Jul 5, 2010 #5
    Re: Paraboloid

    The integral isn't correct.
    Your left-most integral bounds shouldn't have variables in it.
    Your right-most shouldn't have constants.
    You have used "z=" in two of the integrals, and "y=" in none.
     
  7. Jul 5, 2010 #6

    vela

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    Re: Paraboloid

    You have the integrals backwards, and I assume where you wrote z=0, you meant y=0. You have dy on the end, so its limits should be on the frontmost integral. Similarly, the limits for z should be on the middle integral, and the limits for x on the innermost integral. Other than the wrong order, it looks good.
     
  8. Jul 5, 2010 #7
    Re: Paraboloid

    Ya I meant to write them as dxdzdy, but I was so caught up in trying to use Latex for the first time I didn't even notice I had the order mixed up. Thank you for the help.
     
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