How Do You Integrate the Function 1/x?

[mathwonk]

to me, integral means limit of riemann sums, so integral of 1/x means just that. i.e. it means area under the graPH OF Y = 1/X.

now it is a theorem that this area function has a derivative which equals 1/x, and it is also a theorem that this area functioin behaves like a logarith, hence must be one, but all this is a long story.


By the way I love the following proof:

"Now if the limit exists, which you can see it clearly does by looking at the graph,"


I had always though it difficult to prove this limit exists! Another equivalent argument would be perhaps "which is clear from sticking your finger into the wind,.."

 

[StatusX]

it wasn't a rigorous proof. to anyone familiar with the graph, you know that it is differentiable. to prove this would be tricky, but all i meant to do was show why e is involved in this integral at all, and i did that.

 

[BobG]

By the way I love the following proof:

"Now if the limit exists, which you can see it clearly does by looking at the graph,"


I had always though it difficult to prove this limit exists! Another equivalent argument would be perhaps "which is clear from sticking your finger into the wind,.."

And your point is?

It's in the fine tradition of Pierre Laplace, patron saint of math teachers. As Laplace's translator, Nathaniel Bowditch once said, "I never came across one of Laplace's 'Thus it plainly appears' without feeling sure that I have hours of hard work before me to fill up the chasm and find and show how it plainly appears."

Personally, I just go with George Castanza's "Yada yada yada ..."

 

[SomeRandomGuy]

I'm a mathematics major and we don't use log(x) to mean natural log. Maybe some professors have certain biases over others.

 

[shmoe]

What sort of math courses have you taken so far though? I don't think I've seen log to mean base 10 outside of high school or some texts used in the initial calculus stream (and calculators too I suppose). log is pretty much universally accepted to mean base e, at least when mathematicians are talking to one another (and not first year calculus students).

I haven't seen anyone mention base 2 yet. In some cryptography papers I've read published in computer science journals they used log to mean base 2. It was a convenient choice, but a standard that confused me when I first encountered it.

About the "ln" notation, most of you probably used it in your first calculus course at least. I was taught to pronounce "ln" as "lawn", as were most other students I've run across. I've recently been told this was a Canadian thing and that Americans don't do this. So I've been wondering how other countries teach you to pronounce "ln".

 

[Muzza]

"Ell enn".

 

[TenaliRaman]

well i mostly pronounce it as "ell enn" but if u run across my country , you are going to hear different accentuated versions of it like this "Yull Yunn" :p

-- AI

 

[BobG]

"Ell enn".

I had a girlfriend named Ellen. Then we broke up and she became Ellen ex-girlfriend. I begged her to come back. I bought her gifts. I even differentiated her, to no avail.

Suddenly it occurred how to me that no matter what I did, Ellen would remain constant. So all I really had to do was integrate her: Ellen \int ex-girlfiend

 

[fannemel]

now, i have always thought that in mathematics you had to be consistent, is ellen girlfriend or girlfiend?

 

[Chrono]

Suddenly it occurred how to me that no matter what I did, Ellen would remain constant. So all I really had to do was integrate her: Ellen \int ex-girlfiend

I like that. You really must have been thinking about her to come up with that.

 

[abia ubong]

int of x!

how about integrating x!

 

[abia ubong]

integrate x!

how abot integrating x!

 

[abia ubong]

it"s simple and short

inx answer