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Looks stucked

  1. Sep 22, 2004 #1
    I am performing the numerical integration of finding the area of 1/x dx from 0 to 2... using Simpson's rule of n = 6. What will I do in this problem like this since 0 to be evaluated in the f(x) = 1/x is undefined?
     
  2. jcsd
  3. Sep 22, 2004 #2

    matt grime

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    I'd check the question since the integral doesn't exist.
     
  4. Sep 22, 2004 #3

    JasonRox

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    I'm sure it does.

    The integral(anti-derivative) is ln x.

    I'm pretty darn confident that's what it is. I'd prove it, but I'm not in the mood to spend time on here, and last time I tried Latex it didn't work.

    y = ln x

    dy/dx = 1/x
     
  5. Sep 22, 2004 #4

    mathwonk

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    if you are so concerned about your time why are you wasting ours?
     
  6. Sep 23, 2004 #5

    Tide

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    Yes, but what is the value of ln(x) when x = 0? Even if you try to avoid that limit of integration your answer will diverge as you move your endpoint closer to x = 0.
     
  7. Sep 23, 2004 #6

    matt grime

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    the integral, as an improper riemann integral (limit h to zero of int from h to 2) does not exist, Jason. The function has an antiderivative, and that can be used to prove this fact.
     
  8. Sep 23, 2004 #7

    JasonRox

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    Relative to me, your time is going slow, so you might as well take advantage of it. :biggrin:

    Kidding.

    Sorry, I was getting ready to go to bed, and Latex in fact didn't work last time.

    Should of checked my answer, and yes it is wrong.
     
  9. Sep 25, 2004 #8
    You can still use Simpson method,though the integral is improper,by taking the limits of the integral as being from 'a' to 2 (where 'a' tends to 0).Finally take the limit for a->0 from the expression in 'a' obtained after applying Simpson's method.The results is ∞,the integral diverges.
     
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