Originally Posted by

**Canadian0469** I'm not sure if my title makes any sense... sorry, it has been a while since I've done cal.

I'm taking a Probability course and I'm reading one of my profs solutions that involves finding the moment-generating function of a continuous random variable. During the integration steps I got lost. Can someone please help understand how he gets from one step to another (I'll just include the part that confuses me):

$\displaystyle

\int^\infty_0 e^{ty}\alpha{e^{-\alpha y}} dy$

$\displaystyle

= \lim_{k\to\infty}\int^k_0 {\alpha}e^{\left({t-\alpha}\right)y}dy

$

$\displaystyle = \lim_{k\to\infty}[\frac{\alpha}{t-\alpha}e^{\left({t-\alpha}\right)y}]|(y=k,y=0)

$