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Homework Help: Work done by a force field

  1. Apr 27, 2008 #1
    1. The problem statement, all variables and given/known data

    Use Green's Theorem to calculate the work done by the force field

    F = <5x2y3, 7x3y2>

    in moving a particle counterclockwise once around the triangle with vertices (0, 0), (3, 0) and 0, 6).



    2. The attempt at a solution

    I must integrate 6x2y2 over the triangle, right? I then get 1944 as the answer, but the correct answer is 972/5. What is wrong?
     
  2. jcsd
  3. Apr 27, 2008 #2

    Dick

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    Yep, you got it set up all right. But I do get 972/5 for the double integral of 6*x^2*y^2 over the triangle. Check that again. Post how you worked it out if you can't get it.
     
  4. Apr 27, 2008 #3
    OK, i integrate with respect to y first, which gives 2x^2*y^3. The limits are y=0 and y=2x, so I now have to integrate 16x^5 with respect to x. This gives (8/3)x^6, and the limits are x=0 and x=3, so that the answer is 1944.
     
  5. Apr 27, 2008 #4

    Dick

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    y=2x isn't one of the sides of your triangle. y=6-2x is. Draw a picture.
     
  6. Apr 27, 2008 #5
    Lol, thanks!
     
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