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Math Help - Improper Integral

  1. #1
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    Improper Integral

    The initial problem is to find whether

    from 0 to \pi \int\frac{7 - sin(\alpha)}{\alpha^2} converges or diverges. I found that it diverges.

    Then the second part of the problem asks:


    Which of the following inequalities can be used to help prove your conclusion?




    I think it's the first option because the integral I'm comparing to has to be bigger than the original one for it to have any meaning, but should it be

    \frac{6}{\alpha^2}?

    Or is that entirely wrong? I have no idea how to determined which inequality it should be.

    Thank you for any help, and if you could explain a little of how you determined which one it was, I'd really appreciate it.
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  2. #2
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    Krizalid's Avatar
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    just a limit comparison test with \int_0^\pi\frac{d\alpha}\alpha.
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  3. #3
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    I don't understand what that means, sorry. Could you explain?
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  4. #4
    Math Engineering Student
    Krizalid's Avatar
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    have you ever taught the limit comparison test? it's pretty useful when you do not find the appropriate inequality for your integral.
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  5. #5
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    Is that where you replace infinity with "b" and take the limit as b goes to infinity of the integral? If so, yes I know that. That's partially how I determined that the integral diverges.

    I just don't understand the second part...
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