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Integrals 4

  1. Jan 25, 2012 #1
    1. The problem statement, all variables and given/known data

    Use Green's Theorem to calculate [itex]\int F dr[/itex]

    2. Relevant equations

    [itex] F(x,y)= (\sqrt x +y^3) i + (x^2+ \sqrt y) j[/itex] where C is the arc of y=sin x from (0,0) to ( pi,0) followed by line from (pi,o) to (0,0).



    3. The attempt at a solution

    We have [itex]\int f dx + g dy = \int \int_R (g_x-f_y)[/itex] dA for counterclockwise rotation, but the question is given in clockwise rotation so does green's theorem become

    [itex]- \int \int_R (g_x-f_y) dA[/itex]...? Ie, a sign change?
     
  2. jcsd
  3. Jan 26, 2012 #2
    Any clues on this one?

    Thanks
     
  4. Jan 26, 2012 #3

    SammyS

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    Yes, clockwise gives the opposite sign compared to counter-clockwise.
     
  5. Jan 26, 2012 #4
    Thanks
     
  6. Jan 26, 2012 #5
    Can anyone confirm this integral is set up correctly?

    [itex]\displaystyle \int_0^ {\pi} \int_0^ {sin x} (3y^2-2x) dy dx[/itex]
     
  7. Jan 26, 2012 #6

    SammyS

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    That looks OK to me.
     
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