I am a physicist, not a mathematician.(adsbygoogle = window.adsbygoogle || []).push({});

This problem has bothered me for 40 years.

All introductory Calculus texts would consider this integral divergent.

An example found in many texts is the integral of 1/(x-2) from 0 to 3, which is just a variant to the question I am asking. What I find interesting is the accompanying statement that says if you find the integral equal to -ln|2| you would be making a terrible mistake????.

Now back to my problem of the area under the curve of 1/x from –1 to 1.

Using a symmetry argument I would state to however close to the Y axis you want to come the area is exactly equal to 0.0. Even a bigger computer would yield the same sum, exactly 0.0.

Now I know I’m using the word area under the curve and not integral, but I do have an infinite number of Riemann Sums missing only the last sum at X=0,

Not sure what to do with this last sum? But again I can make a strong argument that last Sum is also 0.0 based on symmetry.

I’ll gladly accept any help on this as I am now teaching math, and I want to cover this in my calculus class.

Dr Bob

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# Improper integral of 1/x from –1 to 1

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