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Triple integral, 2 parabolic cylinders

  1. Jul 4, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the volume of the region which is bounded by the parabolic cylinders y=x², x=y² and z=x+y and z=0

    2. Relevant equations

    3. The attempt at a solution

    I solved x=y² for y, and set that equal to y=x², and I got the intersection of the two parabolic cylinders to be at x=1. So I set it up as follows

    ∫∫∫ dzdydx R={(x,y,z)l 0<x<1,x²<y<sqrt(x), 0<Z<x+y}

    (Preted my < are actually < and equal to signs)

    I was wondering if someone could tell me if my set up is correct.

    Thank you.
  2. jcsd
  3. Jul 5, 2010 #2


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    Science Advisor

    Yes, that's exactly right.

    By the way, "LaTex" is much nicer. On this board
    [ tex ]\int_{z=0}^{x+y}\int_{y=x^2}^{\sqrt{x}}\int_{x= 0}^1 dxdydz [ /tex ]
    gives (without the spaces inside [ ])
    [tex]\int_{z=0}^{x+y}\int_{y=x^2}^{\sqrt{x}}\int_{x= 0}^1 dxdydz [/tex]

    Some other boards use "[math] [/math]" or "\( \)" or other things as delimiters but the codes are the same.
  4. Jul 5, 2010 #3
    Ok I will try that next time. Thank you so much.
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