Improper Integral

  1. 1. The problem statement, all variables and given/known data
    Determine if the integral converges or diverges?
    it;s the integral of 0 to infinity
    of 1/(1+x^6)^(1/2)

    2. Relevant equations

    so I compared it with 1/x^2

    3. 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...
  2. jcsd
  3. Dick

    Dick 25,913
    Science Advisor
    Homework Helper

    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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