Why the at term on the exponential turned positive

1. May 14, 2009

Firepanda

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

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?

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

Thanks!

2. May 14, 2009

dx

What is |t| when t is negative?

3. May 14, 2009

Firepanda

positive, ah I see now, thanks

still stuck on 2nd though

edit: actually why would that change the sign of the a?

4. May 14, 2009

dx

Just split the integral into two parts, one on (-∞,0) and the other on (0,∞).

5. May 14, 2009

Cyosis

You should really draw $f(t)=e^{|t|}$. And then give a function that represents f(t) in the first quadrant and f(t) in the second quadrant.

6. May 14, 2009

dx

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