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Homework Help: Integration of -e^(-absval(x))

  1. Mar 19, 2009 #1
    1. The problem statement, all variables and given/known data and equations
    Find [tex]\int[/tex] -1e-|x| between negative infinity and positive infinity.

    2. The attempt at a solution

    So I tried to just integrate using laws for logarithmic equations and got:
    e-|x| between negative infinity and positive infinity.
    Of course this leaves me with:
    e-∞-e-∞ = 0
    I know the answer is -2, but I am not sure how to get there. Help would be much appreciated.
  2. jcsd
  3. Mar 19, 2009 #2


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    Gold Member

    Try splitting the integral into two separate integrals over two separate domains.

    Use the fact that |x| = -x when x<0 and |x|=x for x>0.
  4. Mar 19, 2009 #3
    Thanks danago, I think i figured it out. I split the integral and added the integral of the function from 0 to infinity with -infinity to 0. The first one came out to -1 and the next came out to 1 respectively, giving me -2. I fail to see how I should have caught this before though since the function is defined at 0. I guess you could see that is symmetric and just double the integral from 0 to infinity?
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