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Find The Region

  1. Apr 14, 2009 #1

    aks_sky

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    Find the region enclosed by one leaf of the function r=2 sin2θ


    Now i know how the diagram looks like for this function.
    The diagram can be obtained by using :

    x= r cosθ = 2 sin2θ cosθ
    y= r sinθ = 2 sin2θ sinθ

    Now i have to find the region enclosed by one of the leaves which i am not able to do.
    I know i have to use the jacobian and also that i can use the above as cylindrical coordinates but what do i integrate? i dont know which function to integrate.

    Any Suggestions for that??

    thank you
     
    aks_sky, Apr 14, 2009
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  3. Apr 14, 2009 #2

    rootX

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    [tex]\frac{1}{2}\int r^{2} .d\theta[/tex]

    You can use that formula
     
    rootX, Apr 14, 2009
  4. Apr 14, 2009 #3

    berkeman

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    Staff: Mentor

    Wouldn't it be [tex]\int r d\theta[/tex]

    I could be missing something of course...
     
    berkeman, Apr 14, 2009
  5. Apr 15, 2009 #4

    aks_sky

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    Is the half for finding each half of the region of the leaf?
     
    aks_sky, Apr 15, 2009
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