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Why the at term on the exponential turned positive

  1. May 14, 2009 #1
    Firstly, I don't get why the at term on the exponential turned positive (red arrow).. can someone explain that please?

    291kgae.jpg




    And how do I start on this? How do I split it up such that I can do it for t>0 and t=<0?

    2li8pef.jpg

    Do I just integrate e^2t between -inf and 0 and integrate e^-t between 0 and inf?


    Thanks!
     
  2. jcsd
  3. May 14, 2009 #2

    dx

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    What is |t| when t is negative?
     
  4. May 14, 2009 #3
    positive, ah I see now, thanks

    still stuck on 2nd though

    edit: actually why would that change the sign of the a?
     
  5. May 14, 2009 #4

    dx

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    Just split the integral into two parts, one on (-∞,0) and the other on (0,∞).
     
  6. May 14, 2009 #5

    Cyosis

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    You should really draw [itex]f(t)=e^{|t|}[/itex]. And then give a function that represents f(t) in the first quadrant and f(t) in the second quadrant.
     
  7. May 14, 2009 #6

    dx

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    |t| = -t by definition when t is negative.
     
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