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Homework Help: Stoke's Theorem

  1. Dec 13, 2009 #1
    1. The problem statement, all variables and given/known data
    Let C be the triangle from (0,0,0) to (2,0,0) to (0,2,1) to (0,0,0) which lies in th plane z=y/2. If F(x,y,z)=-3y^2i+4zj+6xk, calculate integral of C F dot dr using Stoke's Theorm.


    2. Relevant equations
    For the curl of F, I obtained -4i-6j+6yk.
    For N, I obtained 0i-1/2j+k.
    0 greater than equal to X greater than equal to 2.
    0 greater than equal to Y greater than equal to 2-x.


    3. The attempt at a solution
    For F dot N, I obtained 3-6y.
    Integrated dydx.
    After integration, I obtain -2; however, I believe the answer is 14.
    What is going wrong?
     
  2. jcsd
  3. Dec 13, 2009 #2

    tiny-tim

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    Hi Dustinsfl! :smile:
    No, you're only using half the curl formula. :wink:
     
  4. Dec 13, 2009 #3
    What is the other half then?
     
  5. Dec 13, 2009 #4

    tiny-tim

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    eg ∂Fz/∂y - ∂Fy/∂z
     
  6. Dec 13, 2009 #5
    Here is what I obtained then (0-4)i-(6-0)j+(0--6y)k which simplified to -4i-6j+6yk
     
  7. Dec 13, 2009 #6

    tiny-tim

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    oops!

    Sorry, I'm being daft. :redface:

    Your curl is correct.

    But shouldn't this be 3+6y ? …
     
  8. Dec 13, 2009 #7
    Yes that was the problem. I have 14 now, thanks.
     
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