In article <firstname.lastname@example.org>, email@example.com (Horst Kraemer) wrote:
> On 9 Apr 2000 05:51:39 GMT, "AC" <firstname.lastname@example.org> 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.