- #1
robert spicuzza
- 9
- 0
I am a physicist, not a mathematician.
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
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