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Finding Volume triple integral by change of variables

  1. Oct 1, 2012 #1
    1. The problem statement, all variables and given/known data

    ∫∫∫V 9z2 dxdydz, where V is the solid defined by:

    -1≤x+y+3z≤1, 1≤2y-z≤7, -1≤x+y≤1

    2. Relevant equations

    3. The attempt at a solution
    I did this using the bounds, 1/3(-x-y-1)<=z<=(1/3)(-x-y+1), -x-1<=y<=1-x, -3/2<=x<=1/2 but I think the answer is wrong is there a better way to do this with change of variables? Thanks, any help would be greatly appreciated.
  2. jcsd
  3. Oct 1, 2012 #2


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    Gold Member

    Well, u = x+y+3z, v = 2y-z, w=x+y would surely give constant limits.
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