The problem involves evaluating a double integral using a change of variables defined by \( u = x + y \) and \( y = uv \). The original integral is set over a triangular region in the xy-plane, specifically the lower half of the unit square.
Some participants have provided insights on how to approach the transformation of the region and suggested examining boundary points to aid in understanding the mapping to uv space. There is ongoing exploration of the relationships between the variables and the implications for the integral.
Participants note the challenge of determining the exact bounds for the new variables and the necessity of understanding the geometry of the region under the transformation.
Yes, you can solve u=u(x,y) and v=v(x,y). Then choose points on the boundary of the domain in xy space and see what the corresponding point is in uv space. A point in the interior of the domain in xy space will point you towards the interior of the region in uv space.V0ODO0CH1LD said:the region looks like a triangle, basically the lower half of the unit square. But how do I transform this region into uv space? I tried to solve the equations of change of variables until I either got the bounds of ##u## as two numbers and the bounds of ##v## at least in terms of ##u##. Or the other way around.. I figured I could solve the integral either way.