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purplemouse

  • 2 years ago

Testing for convergence or divergence of an integral: Use the direct comparison test or limit comparison test to test the integral for convergence. integral (0 to 1) of dt/(t-sint) How do I know which test to use, and how should I proceed from there?

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  1. Rogue
    • 2 years ago
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    I wish I had my calculator on me :( Try comparing it to 1/t.

  2. purplemouse
    • 2 years ago
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    does it matter whether I compare it to 1/t versus 1/t^2 or 1/t^3, etc?

  3. Rogue
    • 2 years ago
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    Yep, this diverges ;) 1/(t - sin t) > 1/t from t:[0,1] \[\int\limits_{0}^{1} \frac {dt}{t} = \left[ \ln t \right]_{0}^{1}\] That is divergent. Since 1/t (the smaller function) diverges, then 1/(t- sin t) (the bigger function) must diverge as well.

  4. Rogue
    • 2 years ago
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    It doesn't matter for this case, but for other integrals, you might wanna choose carefully.

  5. purplemouse
    • 2 years ago
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    I see. thanks. Could I use LCT for this integral as well?

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