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?
An integral with transformations involves changing the coordinates of an integral to simplify the calculation or to better understand the underlying geometric structure.
An integral with transformations can help define the bounds of the integration by transforming the variables to a more easily defined region.
The equation x + y + z = 1 represents the boundary or limit of the region being integrated over. In this case, it acts as a constraint for the values of x, y, and z that can be used in the integral.
To determine the bounds, one can use a change of variables to transform the integral into a simpler form, such as a double or triple integral, and then use geometric or algebraic methods to find the bounds of the new variables.
Some common examples of transformations used in integrals include substitution, polar coordinates, cylindrical coordinates, and spherical coordinates.