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Homework Help: Line integral with green's theorm

  1. Dec 14, 2007 #1
    i would like to find the area bounded by the curve


    i used the substitution given x=(ar)cos(theta) and y=(ar)sin(theta)

    i get :


    thus r^4=xy/(c^2)
    substituting x=(ar)cos(theta) and y=(ar)sin(theta) on the right hand side, i get

    then r^2=ab(cos<theta>)(sin<theta>)/c^2

    then i used jacobian to transform dxdy to drd(theta):

    i get abr(dr)(d(theta))

    then i carried out the double integral
    -- --
    / /
    / / abr(dr)(d(theta))
    -- --

    but i get 0. please advice
    Last edited: Dec 14, 2007
  2. jcsd
  3. Dec 14, 2007 #2
    image not working for me.

    i'd recommend putting in a little bit of time to learn what you need to about latex to be able to post your problem. knowing latex is important if you intend on publishing research papers, anyway.
  4. Dec 14, 2007 #3
    thx for telling me about the image not working, i have posted the question in typed form, please take a look. thx.
  5. Dec 15, 2007 #4
    i just skimmed your work and noticed that you had


    dxdy = drd\theta


    the correct relationship is


    dxdy = rdrd\theta

  6. Dec 15, 2007 #5


    \mbox{let} x=ar\cos\theta \mbox{and} y=ar\sin\theta



    ....wait a minute, why does your first equation not have the terms squared, but then after the substitution, they are squared again?
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