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Volumes with triple integrals, aka I suck at geometry

  1. May 28, 2013 #1
    1. The problem statement, all variables and given/known data

    Calculate the volume of the body that is bounded by the planes:

    x+y-z = 0
    y-z = 0
    y+z = 0
    x+y+z = 2

    2. Relevant equations



    3. The attempt at a solution

    I made a variable substitution

    u = y+z
    v = y-z
    w = x

    which gave me the new boundaries

    u+w = 2
    v+w = 0
    v = 0
    u = 0

    Problem is, I must have slept late the day they taught this is class. What do I do to determine which way these inequalities go?!?
     
  2. jcsd
  3. May 28, 2013 #2
    Do you think you need calculus?

    $$z=x+y \\ z= -x -y +2 \\ z=y \\ z=-y$$

    That should be pretty simple...:tongue:
     
  4. May 28, 2013 #3

    verty

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    Homework Helper

    You should not change variables before you have set up the integral. Do that first.
     
  5. May 28, 2013 #4

    haruspex

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    Gold Member
    2016 Award

    To get an idea of the shape, try to find the vertices.
     
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