Question

Determine whether the improper integral converges, and if so, evaluate it.

Answer 1

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

Answer 2

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

Answer 3

what were the new bounds?

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

ahh gotcha. thanks!