## cherrilyn 5 years ago Determine whether the improper integral converges, and if so, evaluate it.

1. cherrilyn

$\int\limits_{5}^{6} dx/(x-5)^{3/2}$

2. dumbcow

$=\frac{-2}{\sqrt{x-5}}$ from 5 to 6 =-2 - (-infinity)=infinity so it diverges

3. cherrilyn

what were the new bounds?

4. dumbcow

what do you mean? im sorry i used the bounds 5 to 6, and technically took the limit as x goes to 5

5. cherrilyn

aren't the limits supposed to include an infinity somewhere or no?

6. dumbcow

not always it depends on the problem, since our problem has bounds already of 5 and 6 we are checking the limit of the integral from a to 6 as a ->5

7. cherrilyn

ahh gotcha. thanks!