Integrals over an infinite interval

[Aki]

I have this function f(x)=1/x . What would be the intergral from x=1 to x=infinite. Is there a way to calculate that? Because after a while, f(x) would have become so small that it won't matter much.

[maddog]

Originally Posted by Aki

I have this function f(x)=1/x . What would be the intergral from x=1 to x=infinite. Is there a way to calculate that? Because after a while, f(x) would have become so small that it won't matter much.

Yes, this is possible. Because you are starting at 1 you really can have a definite integral
on both sides like so

phi(x) = lim x-> 00 integral {1, 00; (1/x) dx} <== I'm using 00 to kinda' look like infinity.

I think were to take the limit as x goes to infinity that the integral will diverge. To test
this, use L'Hopital's rule (2nd semester calculus). This should work.

Maddog

[Thelonious]

As maddog said, you can find the definite interval, which uses a limit as the number of subintervals approaches infinity.

If you are unfamiliar with this concept, hop on over to Math World for a more in depth analysis, which is too hard to do over this medium.

[sanctus]

you can already be sure that it will diverge knowing that the sum to infinity over 1/n diverges....

[Tim_Lou]

would it be possible so integrate 1/x from 0 to whatever?
it is suppose to be undefined... since the "sum" at 0 is undefined.

but there is a certain area... so, would it be the area of it? or undefined?