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Volume by triple integral

  1. May 17, 2010 #1
    1. The problem statement, all variables and given/known data
    use triple integral to find the volume of tetrahedron enclosed by the coordinat planes "x=o , y=0 , z=0" and the plane 2x+y+z=0

    2. Relevant equations

    3. The attempt at a solution

    I will integrate the constant function f(x,y,z)=1 by the order : dzdydx

    the equation will be : z=-2x-y
    so the limits for the inner integral will be from 0 to -2x-y

    when z=0 ---> y=-2x
    so the limits for the middle integral will be from 0 to -2x

    when z=0,y=0 ---> x=0 .. !!!!
    so the limits for the outer integral will be from 0 to 0 .. !!
    and this means the triple integral will be 0 .. !!
    so there is no volume ??!
  2. jcsd
  3. May 17, 2010 #2
    I think there is a mistake in the plane's equation, right ?
    If I find the x&y&z intercepts, all will be (0,0,0)
    so there is no plane !
  4. May 17, 2010 #3


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    Science Advisor
    Homework Helper
    Gold Member

    These type of homework problems typically ask for the volume in the first octant ...

    Your plane doesn't pass through the first octant because of the 0 on the right side of the equation. To get three positive intercepts you need a positive number on the right, then it will form a tetrahedron with the coordinate planes. Check the problem is copied correctly.
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