(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine if the following is improper and convergent, improper and divergent, or proper

[tex]\int \frac{dx}{\sqrt[3]{x^2 - 7}}[/tex]

from 8 to infinity

3. The attempt at a solution

Since I don't know how to integrate it, I believe I would use the comparison theorem. This is where I have trouble. I understand how it works in regards to seeing if it is convergent or not, but I have trouble determining whether I should get a function larger or smaller. Similarly, I have trouble creating that function. I don't have many examples on it.

So, I used: [tex]\frac{1}{\sqrt[3]{x^{3}}}[/tex] [tex]\leq[/tex] [tex]\frac{dx}{\sqrt[3]{x^2 - 7}}[/tex], in which case, since it is ln(abs(x)), it diverges, and therfore the other must also diverge.

I'm not quite sure if I have that right, and if it was ok to just pick a function that was smaller than the other, without somehow deriving it from the first.

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# Convergent or Divergent Integral: Comparison Theorem

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