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Notation issue with the integration of exponents.

  1. Nov 25, 2007 #1
    I'll not go into the details of the full question, because they are irrelevant to my problem.
    Basically I have to integrate
    [tex]\int_{0}^{\infty} exp (\iota\omega-\alpha)t dt[/tex]

    Which is a nice and easy integration, but it's putting in the limits that bothers me.

    I simply wrote the exponent as [tex]((\iota \omega - \alpha)t)[/tex] because I didn't feel like writing an extra minus sign. I see no reason why I could not have written it

    [tex](-( \alpha -\iota \omega )t)[/tex]

    Which gives a finite answer when putting in the limits, whereas the first way of writing it gives an infinite answer.


    Could someone explain why one of these notations are incorrect?
     
    Last edited: Nov 25, 2007
  2. jcsd
  3. Nov 25, 2007 #2

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    Integral[0, inf] exp(at)dt converges, i.e., has a finite value only when a<0.
     
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