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Triple Integral

  1. Aug 10, 2009 #1
    Given the triple integral [tex]\int\int\int_{G}[/tex] xyz dV
    Where G is the region bounded by x=1, y=x, y=0, z=0, z=2.
    How do I evaluate it.
    Please help.
  2. jcsd
  3. Aug 10, 2009 #2


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    Gold Member

    First of all, is there any other constraint on x? I'll assume that x>=0.
    Do you know how to change triple integrals into single-variable integrals?
    The general idea is to first evaluate the integral while pretending that 2 of the variables are constant. Then you use that result to integrate over the other variables.

    In this case it might be easiest to first evaluate the integral in the triangle 0<=x<=1 and
    0<=y<=x while assuming that z is constant. Then integrate that result with z as a variable from 0 to 2. The triangle can be evaluated in a similar way. In other words:
    [tex]I = \int^{2}_{0}(\int^{1}_{0}(\int^{1-x}_{0} xyz dy)dx)dz[/tex]
  4. Aug 15, 2009 #3
    Cheers. I got an answer of 1/3
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