Thread: Help with and improper integral!

1. Help with and improper integral!

I need help to figure out how can i resolve this improper integral, i don't know what to do with the absolute value:

∫e^(-lyl) <--- Where lyl is the absolute value of "y", and evaluated from -∞ to
-∞
There is also a photo attached of the integral. Thanks!

2. Re: Help with and improper integral!

\begin{align*} &\displaystyle \int_{-\infty}^\infty e^{-|y|}~dy = \\ &\int_{-\infty}^0 e^{-|y|}~dy +\int_{0}^\infty e^{-|y|}~dy = \\ &\int_{-\infty}^0 e^y~dy + \int_0^\infty e^{-y}~dy \end{align*}

can you finish it?

3. Re: Help with and improper integral!

Always split integrals with absolute values at the point the interior expression changes sign.

4. Re: Help with and improper integral!

Originally Posted by romsek
\begin{align*} &\displaystyle \int_{-\infty}^\infty e^{-|y|}~dy = \\ &\int_{-\infty}^0 e^{-|y|}~dy +\int_{0}^\infty e^{-|y|}~dy = \\ &\int_{-\infty}^0 e^y~dy + \int_0^\infty e^{-y}~dy \end{align*}

can you finish it?
Yeah man, thank you so much!