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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 6, 2010 #2

    Dick

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    Re: Compute area using divergence and flux??

    If you could find an F such the div(F)=1, that would work, right?
     
  4. Feb 6, 2010 #3
    Re: Compute area using divergence and flux??

    why would the divergence be 1? could you be more specific please?
     
  5. Feb 6, 2010 #4

    Dick

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    Re: Compute area using divergence and flux??

    You are going to integrate the divergence over the surface by computing the flux of F around the curve, right? If div(F)=1 then the integral of the divergence is the integral of 1 over the surface. That's the area. So pick ANY F that has div(F)=1. There's lots of choices.
     
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