Improper Integral

  • Thread starter Lchan1
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  • #1
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Homework Statement


Determine if the integral converges or diverges?
it;s the integral of 0 to infinity
of 1/(1+x^6)^(1/2)

Homework Equations



so I compared it with 1/x^2

The Attempt at a Solution



the answer key says it converges but i think it diverges since the integral of 1/x^2 diverges from 0 to 1...
 

Answers and Replies

  • #2
Dick
Science Advisor
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1/x^2 is WAY GREATER than 1/(1+x^6)^(1/2) near 0. In fact, the latter function is bounded on [0,1]. The fact 1/x^2 diverges near zero doesn't prove your function does.
 

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