Is 1/x Integrable on Intervals Containing 0?

[robertdeniro]

Homework Statement

Prove that 1/x is NOT integrable on any intervals containing 0

Homework Equations

The Attempt at a Solution

would it be sufficient to say that the anti-derivative, ln x, blows up at 0? would this answer be rigorous enough for an analysis course?

or do i have to use some kind of partition argument?

 

[Char. Limit]

You mean you can't say that since 1/x AND ln(x) do not exist at 0, it cannot be integrated over 0?

 

[╔(σ_σ)╝]

I believe you have to show that you can find a partition such that the upper sum is greater than any alpha ( > 0).

Basically, you show that the integral over zero can get as large as you want.

 

[robertdeniro]

sorry, i have to show that its not improper riemann integrable