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Wacky change of variables for Multi integration

  1. Apr 18, 2004 #1
    Wacky change of variables for Multi integration!!!

    Arghh im having diffiiculty with these problems.
    I am having difficulty mastering the LaTeX form--- (things like how to make a double integral etc) so

    if you look at this site


    and look at page 1040 in the text (ch 15.9) the problem in question is number 14...

    I am having a really tough time rewriting the integrand in u,v form with the given transformation. Perhaps there was a mistake in my algebra--- but what would be the way to go about doing this?

    and also for number 20... would the proper transformation be u = x+y and v = x^2 - y^2 ? Or would something else work better.

    Again I apologize for posting a link--- I promise I will take the time to learn LaTeX before I post--- I just have a tough time with Change Of Variables overall.

    Thanks for all your help.
  2. jcsd
  3. Apr 18, 2004 #2
    Oops, make that Page 1048, not 1040---
  4. Apr 18, 2004 #3
    haha nm i figured out 20--- its better to expand the x^2 - y^2 .... makes life good.
  5. Apr 18, 2004 #4
    For #14, I get the intermediate integral

    [tex]2\int_R(u^2 + v^2) \frac{\partial (x,y)}{\partial (u,v)} \, dA[/tex]
    [tex]R: \quad u^2 + v^2 = 1[/tex]

    Which can then be changed into polar coordinates to be evaluated.

    For #20, I'd try the substitutions u = x + y and v = x - y.

  6. Apr 18, 2004 #5
    Wow thanks cookie I got it! The integrand turns out nicely coz the region is a simple circle--- and easily evaluated using polor coordinates!
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