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Compute area using divergence and flux?

  1. Feb 6, 2010 #1
    Compute area using divergence and flux??

    Consider the curve given by g(t) =acos^3(t),asin^3(t), where t is [0; 2pi] and a > 0 is a constant.

    (a) Find the unit tangent and outward normal vectors.
    (b) Compute the area enclosed by this curve.

    I have done part a), and I know that
    flux of F = divergence x area
    but for part b), i m not given a vector field F. so how am I suppose to approach this question and possibly find the divergence (thus the area)? any hint or solution would be much appreciated. ^__^
     
  2. jcsd
  3. Feb 7, 2010 #2

    HallsofIvy

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    Re: Compute area using divergence and flux??

    Since this is in the plane, it is simpler to use Green's theorem rather than the divergence theorem.

    Green's theorem says that
    [tex]\oint (Ldx+ Mdy)= \int\int \left(\frac{\partial M}{\partial x}- \frac{\partial L}{\partial y}\right) dA[/tex]

    The integral on the right will be the area as long as
    [tex]\frac{\partial M}{\partial x}- \frac{\partial L}{\partial y}= 1[/tex]

    One such choice is M(x,y)= x, L(x,y)= 0.
     
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