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Homework Help: Area of a 2D region (Green's Theorem)(?)

  1. Nov 15, 2009 #1
    1. The problem statement, all variables and given/known data
    Calculate the area of the region within x3 + y3 = 3xy. It can be parametrized by [tex]\gamma[/tex]:[0,[tex]\infty[/tex]] [tex]\rightarrow[/tex] R2 with [tex]\gamma[/tex]=<3t[tex]/[/tex]1+t3, 3t2[tex]/[/tex]1+t3>.

    2. Relevant equations

    Area = 1/2 [tex]\int[/tex]x*dy - y*dx

    3. The attempt at a solution

    My plan is to take the curve parametrized by [tex]\gamma[/tex]=<3t[tex]/[/tex]1+t3, 3t2[tex]/[/tex]1+t3> and use the parametric equations as x = 3t[tex]/[/tex]1+t3 and y = 3t2[tex]/[/tex]1+t3. Then i simply just use the equation for area given by Green's Theorem Area = 1/2 [tex]\int[/tex]x*dy - y*dx and compute the integral. Can anyone confirm if this is right or am I way off?
  2. jcsd
  3. Nov 15, 2009 #2


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    That should work like a charm.:smile:
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