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Why the at term on the exponential turned positive

  • Thread starter Firepanda
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  • #1
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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!
 

Answers and Replies

  • #2
dx
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What is |t| when t is negative?
 
  • #3
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What is |t| when t is negative?
positive, ah I see now, thanks

still stuck on 2nd though

edit: actually why would that change the sign of the a?
 
  • #4
dx
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Just split the integral into two parts, one on (-∞,0) and the other on (0,∞).
 
  • #5
Cyosis
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edit: actually why would that change the sign of the a?
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.
 
  • #6
dx
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|t| = -t by definition when t is negative.
 

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