Improper Integral

**lysserloo** · February 16th 2010, 09:58 AM

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.

**Krizalid** · February 16th 2010, 11:42 AM

just a limit comparison test with $\int_0^\pi\frac{d\alpha}\alpha.$

**lysserloo** · February 16th 2010, 11:44 AM

I don't understand what that means, sorry. Could you explain?

**Krizalid** · February 16th 2010, 11:47 AM

have you ever taught the limit comparison test? it's pretty useful when you do not find the appropriate inequality for your integral.

**lysserloo** · February 16th 2010, 02:47 PM

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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