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Which theorem?

  1. May 12, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]\int _c{(x^2 + y + \sqrt{x})dx + (y - x^2 + \sin{y}) dy[/tex]

    2. Relevant equations

    3. The attempt at a solution

    I'm not sure which theorem to use here. Do I use Green's or the Divergence? Even once I get past this I'm not sure that I can get started.
     
  2. jcsd
  3. May 12, 2009 #2

    gabbagabbahey

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    What curve are you supposed to integrate over?
     
  4. May 12, 2009 #3
    Oops!

    C is the curve transversed counterclockwise which is the boundary of the region bounded by the graphs of [tex] y = x^2 [/tex] and [tex] y = x^3 [/tex]
     
  5. May 12, 2009 #4

    gabbagabbahey

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    Parameterize that curve (you'll have to do it piecewise or separate it into two curves) and then follow the same procedure as in your previous path integral question...
     
  6. May 12, 2009 #5
    The part I'm concerned about is the boundaries... How do I find those?
     
  7. May 12, 2009 #6

    gabbagabbahey

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    Where does [itex]y=x^2[/itex] intersect [itex]y=x^3[/itex]?
     
  8. May 12, 2009 #7
    0 and 1?
     
  9. May 12, 2009 #8

    gabbagabbahey

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    Yep.:smile:....So draw your y=x^2 and y=x^3 graphs from x=0 to x=1 to get an idea of what your curve looks like. Then parameterize it and integrate.
     
  10. May 12, 2009 #9
    Groovy.
     
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