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Triple integral

  1. May 7, 2009 #1
    1. The problem statement, all variables and given/known data
    Sketch the solid E bounded by the cylinder x = y^2 and the planes z = 3 and x + z = 1, and write down its analytic expression. Then, use a triple integral to find the volume of E.

    3. The attempt at a solution
    Was wondering if someone could have a go at drawing this sketch? In mine, I thought i did it right but cant seem to obtain an enclosed surface. If x+z=1 was rather x-z=1 i would be able to but cant so far???
     
  2. jcsd
  3. May 7, 2009 #2

    HallsofIvy

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    The plane x+ z= 1 crosses the plane z= 3 when x+ 3= 1 or the line x= -2, z= 3, y= t. It crosses the cylinder [itex]x= y^2[/itex] in the line [itex]x= t^2[/itex], [itex]y= t[/itex], [itex]z= 1- x= 1- t^2[/itex].

    I wonder if you weren't confusing [itex]x= y^2[/itex] with the [itex]y= x^3[/itex].
     
  4. May 7, 2009 #3
    I don't think you NEED to graph this.

    y=(plus/minus) sqrt(x)

    If that helps.

    The range is x>0, so sqrt(x) is real.

    If x>0, which is on top, z=3 or z=1-x?


    EDIt: Is there an upper bound on x?
     
  5. May 7, 2009 #4
    wat i have done is drawn the cylinder x = y^2 in the x-y plane and extended it along the z plane. Then i drew the z=3 plane and then drew a line z=1-x and it extended it along the y plane. But this does not end up enclosing a solid
     
  6. May 7, 2009 #5
    You are right, I think. There must be an upper x-limit for this to be a solid. Maybe, you have accidentally skipped some information.
     
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