The discussion revolves around evaluating a triple integral of the form dxdydz/(y+z) under the constraints x >= 0, y >= 0, z >= 0, and bounded by the equation x + y + z = 1. The original poster mentions specific transformations to be used: x = u(1-v), y = uv(1-w), z = uvw.
The discussion is ongoing, with participants exploring the implications of the transformations and the necessity of including the full problem statement. There is a suggestion that using the original variables might simplify the integration process.
There is a noted concern regarding the clarity of the problem statement and the prescribed transformations, which may affect the ability to determine the integration bounds accurately.
Does the exercise text prescribe this ? Your problem statement doesn't -- could you please post the full problem statement ?Cyn said:The transformations I need to use are x=u(1-v), y=uv(1-w), z=uvw
Cyn said:Homework Statement
I have a question. I need to know the integral dxdydz/(y+z) where x>=0, y>=0, z>=0.Homework 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.
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?
Cyn said:Homework Statement
I have a question. I need to know the integral dxdydz/(y+z) where x>=0, y>=0, z>=0.Homework 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.
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?