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Homework Help: Help integrating

  1. Apr 10, 2005 #1
    the question is "evaluate [tex] \iiint z \,dv[/tex], of a solid tetrahedron bounded by the four planes x=0,y=0,z=0, and x+y+z=1"
    I can set up the problem correctly but i cant seem to integrate it right
    [tex]\int_{0}^1 \int_{0}^{1-x} \int_{0}^{1-x-y} z dzdydx[/tex]
    [tex](1/2) \int_{0}^1 \int_{0}^{1-x} (1-x-y)^2dydx[/tex]
    can somone please show me the last few steps of this problem? :confused:
  2. jcsd
  3. Apr 10, 2005 #2


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    Open the brackets and integrate each term with corresponding limits...

  4. Apr 10, 2005 #3


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    For the evaluation of the inner integral, use the y-anti-derivative :
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