Defenite Integral. Change of Variables.  TOPIC_SOLVED

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Defenite Integral. Change of Variables.

Postby sepoto on Mon Dec 23, 2013 7:13 am

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The calculation for the limit as x approaches infinity is above and it is supposed to be 1/2. I'm trying to figure out how that limit was calculated. The solution for the limit is not really enumerated enough that I can figure out how 1/2 was arrived at.

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Postby stapel_eliz on Mon Dec 23, 2013 2:59 pm

They show all the steps. At which point does the worked solution stop making sense?

Please be specific. Thank you! :wink:
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Re: Defenite Integral. Change of Variables.

Postby sepoto on Mon Dec 23, 2013 9:39 pm

The limit as x approaches infinity of the definite integral below (I hope I have the right definite integral, there are two others to choose from in this problem):



My solutions manual shows the result of the calculation to be:


The part I don't understand right now is how this was calculated:


I don't see how was reached. I don't see how was arrived at either. Could someone fill me in on how that limit was calculated?

Thank You!
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  TOPIC_SOLVED

Postby stapel_eliz on Mon Dec 23, 2013 10:21 pm

The exercise statement gives you the following:

. . . . .

So there is no "computation" or "figuring" to do. This is just something you are given. You are also given the integral expression for E(x) as being something that occurs in probability and statistics. For the origin of this expression, you'd likely need to study probability or statistics.

In other words, there's nothing to figure out or compute or develop or explain; you're just using what they've given you.

Note: There appears to be a typo in the solution, as the in the original expression suddenly changes to at the end of the worked solution to part (a), which of course would prevent the simplification to . Draw in the square-root symbol, and the proof should be fine. :wink:
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