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Very quick question

  1. Jun 20, 2005 #1
    [itex] \forall n > 0,\;n \in \mathbb{R} [/itex], does
    [tex] \int\limits_n^\infty {\frac{{\sin x}} {x}dx} [/tex]
    converge? If so, to what?
  2. jcsd
  3. Jun 20, 2005 #2


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    It's a function of "n".It converges for every possible "n".

    [tex] \int_{n}^{\infty} \mbox{sinc} \ x \ dx =\frac{\pi}{2}-\mbox{Si}\ (x) [/tex].

  4. Jun 20, 2005 #3
    hello there

    well I have attached a plot of the intergrand, as you would see the function converges to 0 and should be integrable


    Attached Files:

  5. Jun 20, 2005 #4
    you can prove that it converges by multiplying the integrand by 1 (in this case pick x/x or x^2/x^2 or something) & use integration by parts, & then the comparison test. i don't think that helps find what it converges to but judging by the image it looks like it goes to 0.
  6. Jun 21, 2005 #5
    Hey um, where can I download/get this program? :redface:
  7. Jun 21, 2005 #6


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    What program...?

    "sinc" is graphed in a ton of books.It's even in physics books when discussing Fraunhofer diffraction from single or multiple slits.

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