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Multiple Integration

  1. May 6, 2007 #1
    I'm having problems finding the limits for the follwing integration, can anyone help?

    Find the volume bounded by x+2z=4 and 2y+z=2 with x,y and z>=0
  2. jcsd
  3. May 6, 2007 #2
    I think the following limits apply but can't find the upper one for z, or in which order they should go.

    x: 0 -> 4-2z
    y: 0 -> 1-0.5z
    z: 0 -> ????
  4. May 6, 2007 #3


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    Staff Emeritus
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    It seems like if you pick any z>=0, you can find x,y that satisfy the boundary condiitions. Hence, z should be between 0 and [tex]\infty[/tex]
  5. May 6, 2007 #4

    D H

    Staff: Mentor

    There are five boundary conditions:
    1. x+2z<=4
    2. 2y+z<=2
    3. x>=0
    4. y>=0
    5. z>=0

    Picking a value for z beyond some finite limit will not work.
  6. May 6, 2007 #5
    So z <= 2!

    Thank you so much.
    Last edited: May 6, 2007
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