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Change of vaiables. Jacobians

  1. Dec 4, 2006 #1
    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. jcsd
  3. Dec 4, 2006 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    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
  4. Dec 4, 2006 #3
    Thanks

    Thanks, that put me back on track!
     
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