# Thread: Trouble on Integral Test

1. ## Trouble on Integral Test

Hi guys! I was doing a problem for my homework and I was doing great until the end. I got the integral correct and proved that the series converged but I'm having trouble understanding something. In the attached picture: I just need some explanation from at the point the limit is set up from t -> infinity and why they then set up another limit from s -> 0 and why for that latter portion they somehow got an e8. Thanks for all your help guys!

2. ## Re: Trouble on Integral Test

That is an s, not an 8. It is $e^s$.

3. ## Re: Trouble on Integral Test

If \displaystyle \begin{align*} s = \frac{11}{t} \end{align*} then as \displaystyle \begin{align*} t \to \infty , \, s \to 0 \end{align*}...

4. ## Re: Trouble on Integral Test

omg, i legitimately couldn't tell. thanks so much!