# Change of vaiables. Jacobians

1. Dec 4, 2006

### robierob

I need to find out how to solve this integral with the indicated changes/transformations.

int.[0 to 2/3]int[y to 2-2y]
(x+2y)e^(y-x)
dxdy

u=x+2y v=x-y

I know that the xy region is x=y y=0 and y=1- (x/2)
which is a triangle

so I created systems with U and V but cant get a new bounded region...

I just get u=v and two other lines that intersect at the origin.
If anyone can tell me whats up with this it would be helpfull.

Also, does it seem weird that my given v doesnt match the problem exactly?
the u and v were given changes.

Last edited: Dec 4, 2006
2. Dec 4, 2006

### HallsofIvy

Staff Emeritus
What does the region look like in the xy-coordinate system?

One line is y= x. If v= x- y, what is v on that line? Another line is y= 1- (1/2)x or 2y= 2- x so x+ 2y= 2. What is u on that line? Finally, the third line is y= 0. In that case, u= x and v= x so y= 0 corresponds to the line u= v. What does that look like in the uv-coordinate system?

Last edited: Dec 4, 2006
3. Dec 4, 2006

### robierob

Thanks

Thanks, that put me back on track!