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Math Help - Integral of sech(x) between infinity and minus infinity

  1. #1
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    Integral of sech(x) between infinity and minus infinity

    As the title says, I am trying to find the definite integral of sech(x) with limits of infinity and minus infinity.

    I always get 2pi as my solution, but all calculators and integration applets give pi as the answer.

    Below is my method so far:


    Could someone please tell me where I have gone wrong?

    EDIT: there is an error in line 6 of my method, that extra u is just a typo.
    Last edited by incblue; May 8th 2011 at 04:46 AM. Reason: Small error in image posted
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    You didn't change your terminals when you substituted u. Also, your integrand should be 1/(u^2 + 1), not u/(u^2 + 1), but since you have integrated this correctly I suspect that is just a typo.
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    You didn't change your terminals when you substituted u.
    I did, but e^infinity is just infinity.

    Also, your integrand should be 1/(u^2 + 1), not u/(u^2 + 1), but since you have integrated this correctly I suspect that is just a typo.
    Yes, that was a typo. I had mentioned it in an edit prior to your post.


    Anyway, I still have the issue of 2pi versus pi.
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    Quote Originally Posted by incblue View Post
    I did, but e^infinity is just infinity.
    But \displaystyle \lim_{x \to -\infty}e^x = 0, not \displaystyle -\infty...
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