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Improper Integral 
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#1
Feb809, 03:48 PM

P: 39

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
Feb809, 04:17 PM

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P: 25,247

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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