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tomiko

when is it impossible to find the definite integral of a function?

  • one year ago
  • one year ago

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  1. Mani_Jha
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    If the function doesn't exist in an interval. For example, \[\int\limits_{-1}^{0}\ln xdx\] is meaningless. log is defined only for positive numbers

    • one year ago
  2. tomiko
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    so when i have a question like the above i can just state it's impossible find the def integral of the this function?

    • one year ago
  3. Mani_Jha
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    yes, stating the reason if possible

    • one year ago
  4. tomiko
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    great! thanks. :). can you give another instance where it's impossible to find the integral?

    • one year ago
  5. TuringTest
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    Some integrals, like\[\int_a^b e^{-kx}x^{-1/2}dx\]and\[\int_a^b\sin(x^2)dx\]have no closed form, and have to be written in terms of the error function

    • one year ago
  6. TuringTest
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    And, as Mani said, if the interval contains a singularity, like\[\int_{-1}^1\frac{dx}x\]is undefined because there is a singularity at x=0. In this case, if you want an answer you can use the Cauchy principle value, which in this case gives 0. In principle though, this integral does not converge.

    • one year ago
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