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Riemman summs

  1. Apr 26, 2010 #1
    there is correct the expresion [tex]\int^{-\pi+\epsilon}_{\pi-\epsilon} d\theta[/tex]....where [tex]\theta[/tex] is a angular coordinate between [tex](-\pi,\pi)[/tex]....¿what means this?...

    i believe that this mean that the angular coordinate theta runs from [tex]\pi-\epsilon[/tex] to
    [tex]-\pi+\epsilon[/tex] in the sense anti clock (figure)
     

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  2. jcsd
  3. Apr 27, 2010 #2

    HallsofIvy

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    It's a bit peculiarly written. I would use
    [tex]\int_a^b f(x)dx= -\int_b^a f(x) dx[/tex]
    to write
    [tex]\int_{\pi- \epsilon}^{-\pi+ \epsilon} d\theta= -\int_{-\pi+ \epsilon}^{\pi- \epsilon} d\theta[/tex]

    and it would NOT be the yellow portion of your picture but, rather, the white portion.

    And, if it is really only [itex]d\theta[/itex] itself you are integrating,
    [tex]\int_{\pi- \epsilon}^{-\pi+ \epsilon} d\theta= \left[ \theta\right]_{\pi- \epsilon}^{-\pi+ \epsilon}= -\pi- \epsilon- (\pi- \epsilon)= -2(\pi- \epsilon)[/tex]
    and
    [tex] -\int_{-\pi+ \epsilon}^{\pi- \epsilon} d\theta= -\left[\theta\right]_{-\pi+ \epsilon}^{\pi- \epsilon}= -(\pi+ \epsilon-(\pi- \epsilon))= -2(\pi- \epsilon)[/tex]
    again.
     
  4. Apr 27, 2010 #3
    there is a way that the integral follows the path yelow???'.....i can't to use in my problem [tex]\int_{-\pi}^{-\pi+\epsilon}+\int_{\pi-\epsilon}^{\pi}[/tex] in my problem
     
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