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Math Help - Integration problem

  1. #1
    Senior Member Sambit's Avatar
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    Question Integration problem

    Let, Yn= integration of {e^(-nt)}/t , from 0 to 1, where n is a natural number. what can be said about the sequence {Yn}?

    Pleaze help me for this problem. at least hep me finding the integration part.
    Last edited by mr fantastic; October 18th 2010 at 04:11 PM. Reason: Edited title.
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  2. #2
    A Plied Mathematician
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    Umm, as far as I know, none of those integrals converge. Just to be clear, you do mean that

    \displaystyle Y_{n}=\int_{0}^{1}\frac{e^{-nt}}{t}\,dt, right?
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  3. #3
    Senior Member Sambit's Avatar
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    right. can you please explain your answer?
    also, please tell me what happens if the limit is from 1 to 2.
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  4. #4
    A Plied Mathematician
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    Well, the integral \displaystyle\int_{0}^{1}\frac{1}{t}\,dt does not converge, and

    \displaystyle\int_{0}^{1}\frac{e^{-nt}}{t}\,dt\ge \int_{0}^{1}\frac{e^{-n}}{t}\,dt=e^{-n}\int_{0}^{1}\frac{1}{t}\,dt, assuming n>0.

    So, by the comparison test, you've got yourself a divergent integral.

    [EDIT] If you go with the interval [1,2], then everything in sight is suddenly convergent. But you've got not-so-nice integrals to deal with.
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  5. #5
    Senior Member Sambit's Avatar
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    thanks a lot. and what if the limit is from 1 to 2?
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  6. #6
    A Plied Mathematician
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    See the edit in my previous post.
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  7. #7
    Senior Member Sambit's Avatar
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    ya. got it. thnx.
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  8. #8
    A Plied Mathematician
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    You're welcome. Have a good one!
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