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Re: Finite and infinite areas
Posted:
Apr 9, 2000 3:36 PM
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In article <38f0a8d9.34905717@news.btx.dtag.de>, horst.kraemer@t-online.de
(Horst Kraemer) wrote:
> On 9 Apr 2000 05:51:39 GMT, "AC" <amandioc@clix.pt> wrote:
>
> > Hi.
> >
> > Why is that the area between f(x) and xx axis in the interval , say [1,
> > +infinite]
> > is finite if f(x)= 1/x^2 but infinite if f(x) = 1/x ?
> > I would like an explanation in geometric "visible" terms.
>
> The explanation would be the same as for the question: Why is the sum
>
> 1 + 1/2^2 + 1/3^2 + 1/4^2 + ....
>
> bounded and why isn't the sum
>
> 1 + 1/2 + 1/3 + 1/4 + ...
>
> bounded, too. Sorry, I heard this question a lot of times, but I still
> don't know a better answer than "because it is like that".
>
This strange example gives rise to a solid of finite volume that has a
cross-section of infinite area. You just take the area bounded by the
x-axis and 1/x, from 1 to inifinity, and spin it around the x-axis.
Steve L
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