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Change of Variables - Help!

  1. Sep 21, 2009 #1
    1. The problem statement, all variables and given/known data
    using change of variables, find the region bounded by
    y = x, y = 2x, xy = 1, xy=2


    2. Relevant equations



    3. The attempt at a solution
    i know i have to introduce the variables u, v
    the problem is i don't understand how to introduce them
    i tried read the textbook but the examples all introduce the new variables for you

    i think i understand the steps that follow, im just stuck at the beginning
     
  2. jcsd
  3. Sep 21, 2009 #2

    LCKurtz

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    Well, you would like your uv integral to have constant limits if possible. You have xy=1 and xy=2 so that certainly suggests setting u or v = xy. If you use v, then v will go from 1 to 2.

    Now can you see how to choose u so that y = x and y = 2x give you constant limits for u?
     
  4. Sep 21, 2009 #3
    i guess y/x?
    that'll give me 1 to 2 as well?
     
  5. Sep 21, 2009 #4

    LCKurtz

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    Good guess. I hope it wasn't a pure guess. You don't have to ask about the limits. Look at the equations. And plot your uv region.
     
  6. Sep 21, 2009 #5
    i vaguely remembered a similar example the prof did, i missed how he had chosen u and v, which resulted in my confusion

    thank you so much for the help!
     
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