1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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]

    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


    User Avatar
    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 by a moderator: Dec 4, 2006
  4. Dec 4, 2006 #3

    Thanks, that put me back on track!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook