Integral with transformations and bounded by x + y + z = 1

Tags:
1. May 18, 2017

Cyn

1. The problem statement, all variables and given/known data
I have a question. I need to know the integral dxdydz/(y+z) where x>=0, y>=0, z>=0.

2. Relevant equations
It is bounded by x + y + z = 1. The transformations I need to use are x=u(1-v), y=uv(1-w), z=uvw.

3. The attempt at a solution
y+z = uv. J = uv(v-v^2+uv)
So I get the integral (v-v^2+uv)dudvdw. But I don't know which bounds I need to use. Is this correct and how can I know the bounds?

2. May 18, 2017

BvU

Does the exercise text prescribe this ? Your problem statement doesn't -- could you please post the full problem statement ?

For a start: If you can't write the bounds in terms of u, v and w, can you give them in terms of x, y and z ?

3. May 18, 2017

Ray Vickson

If somebody is forcing you to use the transformation, then I guess you are stuck with it. However, just doing repeated integrations in terms of x, y, z is much more straighforward.

4. May 18, 2017

SammyS

Staff Emeritus
It's a good idea to include the whole problem statement in the main body of you post. If a part of the problem statement is contained in the thread title, please repeat that part in the body of the Original Post.

Integral with transformations and bounded by x + y + z = 1