cherrilyn
  • cherrilyn
Determine whether the improper integral converges, and if so, evaluate it.
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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cherrilyn
  • cherrilyn
\[\int\limits_{5}^{6} dx/(x-5)^{3/2}\]
dumbcow
  • dumbcow
\[=\frac{-2}{\sqrt{x-5}} \] from 5 to 6 =-2 - (-infinity)=infinity so it diverges
cherrilyn
  • cherrilyn
what were the new bounds?

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dumbcow
  • dumbcow
what do you mean? im sorry i used the bounds 5 to 6, and technically took the limit as x goes to 5
cherrilyn
  • cherrilyn
aren't the limits supposed to include an infinity somewhere or no?
dumbcow
  • 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
cherrilyn
  • cherrilyn
ahh gotcha. thanks!

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