Why the at term on the exponential turned positive

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!

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dx
Homework Helper
Gold Member
What is |t| when t is negative?

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?

dx
Homework Helper
Gold Member
Just split the integral into two parts, one on (-∞,0) and the other on (0,∞).

Cyosis
Homework Helper
edit: actually why would that change the sign of the a?
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.

dx
Homework Helper
Gold Member
|t| = -t by definition when t is negative.