For the following two problems, does the integral diverge or converge (if so, to what)

Integral of sinx/(cosx - 1) from -pi/2 to pi/2

Integral of e^x/x from 1 to infinity

Thanks!

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- April 9th 2009, 09:03 PMrainbowkaineConvergent/Divergent Integrals
For the following two problems, does the integral diverge or converge (if so, to what)

Integral of sinx/(cosx - 1) from -pi/2 to pi/2

Integral of e^x/x from 1 to infinity

Thanks! - April 9th 2009, 09:09 PMJhevon
- April 9th 2009, 09:11 PMrainbowkaine
I don't remember. I have not taken Calculus 2 in a while and need this for a friend. An answer would be wonderful. (But my guess is that it diverges since the sum from 1 to infinity of 1/n diverges and e^n/n is larger than that)

- April 9th 2009, 09:18 PMJhevon
- April 9th 2009, 09:21 PMrainbowkaine
So this integral diverges. So do you basically evaluate the given function taking into account the limits and then whatever happens to it happens to the area under the function?

Also, for the first problem, do you tell that it's odd simply by plugging in a test value? And then once you know it's odd, what does it mean that its evaluated over a symmetric interval (I have to be able to explain this tomorrow). Thanks so much for the help! - April 9th 2009, 09:27 PMJhevon
yes. at first i was trying to piggy back on the integral test, but i realize that is not applicable here, since we have an increasing function. thus, we can use an argument similar to what you just gave. the integral gives the net area under the curve, and we have a curve that is diverging to infinity, exponentially so; thus, the area under the curve (and hence the integral) will diverge as well.

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Also, for the first problem, do you tell that it's odd simply by plugging in a test value? And then once you know it's odd, what does it mean that its evaluated over a symmetric interval (I have to be able to explain this tomorrow). Thanks so much for the help!