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Improper integral

  • Thread starter cragar
  • Start date
  • #1
2,544
2

Homework Statement


integral from 2 to infinty 1/(x-sqrt(x))

The Attempt at a Solution


my teacher wants us to compare it to another function in the form 1/x^p
and not integrate it so
would i compare it to 1/x and then do the limit comparison test
limit as x approaches infinity
i came out with a finite number and since 1/x divegres therefore 1/(x-sqrt(x)) diverges
is this correct.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
251
integral from 2 to infinty 1/(x-sqrt(x))

my teacher wants us to compare it to another function in the form 1/x^p
and not integrate it so
would i compare it to 1/x and then do the limit comparison test
limit as x approaches infinity
Hi cragar! :smile:

That'll do, but you don't actually need the limit comparison test in this case, since 1/(x - √x) is always larger than 1/x :wink:
 
  • #3
2,544
2
so you are saying since it is larger than something that diverges then it to will diverge.
i see.
 

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