Work done by a force field

  • Thread starter kasse
  • Start date
  • #1
kasse
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1

Homework Statement



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?
 

Answers and Replies

  • #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.
 
  • #3
kasse
382
1
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.

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.
 
  • #4
Dick
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y=2x isn't one of the sides of your triangle. y=6-2x is. Draw a picture.
 
  • #5
kasse
382
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Lol, thanks!
 

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