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Homework Help: Green's theorem applied to polar graph

  1. Oct 1, 2009 #1
    1. The problem statement, all variables and given/known data

    Use Green's theorem to compute the area of one petal of the 28-leafed rose defined by [tex]r = 5sin(14 \theta)[/tex]
    2. Relevant equations
    [tex] A = \frac{1}{2} \int_c{x dy - y dx}[/tex]
    [tex]\int \int_c{M_x + N_y}dx dy[/tex]

    3. The attempt at a solution

    I'm really more confused about just what to do outright. Green's theorem tells me that I can take the integral in that area formula and compute the double integral of the divergence of a vector field F = <M(x,y),N(x,y)>, but I have no idea how that helps me since I don't see any vector field here and I don't know the components N and M.

    I think maybe I need to turn the expression [tex]r = 5sin(14 \theta)[/tex] into cartesian coordinates, but not really seeing what to do from here.

    theres just too many equalities in greens theorem >:(
  2. jcsd
  3. Oct 2, 2009 #2


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    Science Advisor
    Homework Helper

    Hi csnsc14320! :wink:

    (your equations look a bit odd)

    Hint: you're looking for a function whose curl is constant. :smile:
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