# Convergent or Divergent

• Feb 6th 2013, 09:31 AM
amthomasjr
Convergent or Divergent
$\int_{-\infty}^{-1} e^{-26t}dt$

This is my work:
$\lim_{a \rightarrow -\infty}\int_{a}^{-1} e^{-26t}=\lim_{a \rightarrow -\infty}\left[-\frac{1}{26}e^{-26t}\right]_a^{-1}=\lim_{a \rightarrow -\infty}\left[-\frac{1}{26}\left(e^{26}-e^{-26a}\right)\right]$

$\lim_{a \rightarrow -\infty}e^x =0$ so it would converge to $-\frac{1}{26}e^{26}$ but that's not the correct answer. Can someone explain to me where I went wrong?
• Feb 6th 2013, 10:08 AM
amthomasjr
Re: Convergent or Divergent
I think I know what I did wrong. $(-26)(-\infty)=+\infty$ making it divergent