# integral with absolute value

• April 7th 2008, 10:05 PM
lllll
integral with absolute value
I need some help integrating :
$\int e^{-|y|}e^{ty} dy$
• April 7th 2008, 11:33 PM
Opalg
Quote:

Originally Posted by lllll
I need some help integrating :
$\int e^{-|y|}e^{ty} dy$

You just have to split it up as a sum of two integrals, by considering saparately the intervals on which y is positive and negative:

$\int e^{-|y|}e^{ty}\, dy = \int_{y\leqslant0} e^{y}e^{ty}\, dy + \int_{y\geqslant0} e^{-y}e^{ty}\, dy = \int_{y\leqslant0} e^{(t+1)y}\, dy + \int_{y\geqslant0} e^{(t-1)y}\, dy$