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Improper intergrals

  1. Oct 14, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]$\int_{-\infty}^{0}e^{-|x|}dx[/tex]
    2. Relevant equations

    [tex]$\int_{-\infty}^{0}e^{-|x|}dx[/tex]
    = [tex]$\int_{-\infty}^{0}e^{-x}dx[/tex]

    according to the solution these first two steps is where i go wrong. According to solution, the integral is e^x, which I dont understand. I get e^-x and when I carry out the problem I get -1. The correct answer is 1. Please explain the simplification. thank you
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 14, 2009 #2

    Mark44

    Staff: Mentor

    |x| is defined to be equal to x, if x >= 0, and to -x, if x < 0. Your interval over which your are integrating is the negative half of the real line.
     
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