Why does this converge?

  • Thread starter flyingpig
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  • #1
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Homework Statement



Determine whether the improper integral diverge or converge. If it is convergent, evaluate it with a limit

[tex]\int_{0}^{1}\frac{1}{\sqrt[3]{x}}dx[/tex]


Just from inspection, I thought this was a p-series with 1/3 < 1, but then I noticed the limits of integration is from 0 to 1.

So my question is, is there a way, just from inspection, to notice this is convergent without resorting to any test?
 

Answers and Replies

  • #2
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Just fixed question
 
  • #3
Dick
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It's not a p-series. It's not any kind of series at all. It's an improper integral. Integrate it and take the limit as the lower limit approaches 0.
 
  • #4
SammyS
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It's not a p-series. It's not any kind of series at all. It's an improper integral. Integrate it and take the limit as the lower limit approaches 0.

I.E. Evaluate:

[tex]\int_{a}^{1}\frac{1}{\sqrt[3]{x}}dx[/tex]

Take the limit of the result as a → 0+.
 

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