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cherrilyn

  • 5 years ago

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

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  1. cherrilyn
    • 5 years ago
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    \[\int\limits_{5}^{6} dx/(x-5)^{3/2}\]

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

  3. cherrilyn
    • 5 years ago
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    what were the new bounds?

  4. dumbcow
    • 5 years ago
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    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
    • 5 years ago
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    aren't the limits supposed to include an infinity somewhere or no?

  6. dumbcow
    • 5 years ago
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    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
    • 5 years ago
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    ahh gotcha. thanks!

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