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Problem with improper integrals

  1. Nov 17, 2011 #1
    1. The problem statement, all variables and given/known data

    ∫xe^(-2x)dx from x = 0 to ∞

    2. Relevant equations

    -xe^(-2x)/2 - e^(-2x)/4 + C

    3. The attempt at a solution

    lim b→∞ -x/2e^(2b) - 1/4e^(2b) = 0

    wolfram alpha says its 1/4 and I do not know why (it does not show steps)

    Can you help me?
     
  2. jcsd
  3. Nov 17, 2011 #2

    ehild

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    Homework Helper
    Gold Member

    You did not take the lower limit into account. Substitute x=0 and subtract.

    ehild
     
  4. Nov 17, 2011 #3
    You're right lol I'm dumb... anyway substituting the lower limit I get 3/4 and not 1/4 :/
    -(-1/2 - 1/4) = 3/4
     
  5. Nov 17, 2011 #4
    Thank you
     
  6. Nov 17, 2011 #5
    just saw my mistake... 1/2 should be zero, that way I do get 1/4... thank you again
     
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