Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: Finite and infinite areas
Replies: 17   Last Post: Apr 15, 2000 7:50 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Steve Leibel

Posts: 300
Registered: 12/6/04
Re: Finite and infinite areas
Posted: Apr 9, 2000 3:36 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply



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







Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.