Triple Integral

DrunkApple

1. The problem statement, all variables and given/known data
f(x,y,z) = e^(2x-z)
W: x+y+z ≤ 1, x,y,z ≥ 0

2. Relevant equations
0 ≤ x ≤ 1-y-z
0 ≤ y ≤ 1-x-z
0 ≤ z ≤ 1-x-y

3. The attempt at a solution
I tried dzdydx and dydzdx but they don't work...
or am I doing something wrong?

jambaugh

You will note that the boundaries are symmetric under permutations of x, y, and z. Thus w.r.t. the boundary order of integration shouldn't matter.

The integrand will be quite easy to integrate. I suggest you factor it into e^(2x) e^(-z).

You just have to set up your boundaries of integration correctly. Can you show us some of your attempts?

DrunkApple

Isn't that the correct boundaries that I set up in relevant equations?
or is that wrong?
I would love to post my work... but it's so much mess right now... it's like everywhere... If I can get the right boundaries I feel like I can get it right

jambaugh

Give me what you got....

integral from what to what, from what to what, from what to what of what dwhatdwhatdwhat?