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How do i do this?

  1. Feb 5, 2004 #1
    Find the work (intergral over C )F dot dr done by a force F=yi + xj in going all the wy counterclockwise around circle C give by x^2+y^2+2x=0, by the easiet technique you know.

    Would i get a double intergral over C (-1) dxdy? How would I get C?
     
  2. jcsd
  3. Feb 6, 2004 #2
    U can interchange dy into dx and vice versa from the equation of circle and it will be easy to integrate
     
  4. Feb 6, 2004 #3

    HallsofIvy

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    The easiest way is this: Since d(y)/y= 1= d(x)/dx, this is a "conservative" force field (mathematically, ydx+ xdy is an "exact differential") and so its integral around any closed path is 0.

    I'm not sure where you got "-1" from. Using Green's theorem the integrand would be d(x)/dx- d(y)/dy= 1- 1= 0 just as above.

    Saying "How would I get C?" makes it sound as if you think C is a constant. You don't have to "get" C: C is the path given.

    IF the problem were to integrate, say, ydx+ 3xdy, then we would integrate [tex]\int (\frac{d(3x)}{dx}-\frac{d(y)}{dy})dA [/tex]
    = [tex]2\int dA[/tex] which is just 2 times the area of the circle.
     
    Last edited: Feb 6, 2004
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