Triple Integral Domain

  • Thread starter DrunkApple
  • Start date
  • #1
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1. The problem statement, all variables and given known data
f(x,y,z,) = [itex]e^{2x-z}[/itex]
W: x + y + z ≤ 1
x, y, z ≥ 0


Homework Equations





The Attempt at a Solution


For each domain, could you check it please?
This is the only triple integral that's haunting me

0 ≤ x ≤ 1-y-z
0 ≤ y ≤ 1-x-z
0 ≤ z ≤ 1-z-y
 

Answers and Replies

  • #2
34,687
6,394
1. The problem statement, all variables and given known data
f(x,y,z,) = [itex]e^{2x-z}[/itex]
W: x + y + z ≤ 1
x, y, z ≥ 0


Homework Equations





The Attempt at a Solution


For each domain, could you check it please?
This is the only triple integral that's haunting me

0 ≤ x ≤ 1-y-z
0 ≤ y ≤ 1-x-z
0 ≤ z ≤ 1-z-y
I don't think you're on the right track here, at all. If you haven't already done so, sketch the region over which integration is to be done. The region is a tetrahedron that is bounded by the three coordinate planes and the plane x + y + z = 1. Where this plane intersects the x-y plane will play a role in your description of the region.
 

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