SRL Archive - Mathematics

my mind was blown yesterday when my math teacher defined ln(x) as the integral from 1 to x of 1/x….can someone explain this magic??

also, e is a crazy number…

Also i was wondering how people are doing in BC Calc (if they are taking it) because the average grade on our last test was 62….

Im taking AP Calc AB, but we've covered the derivative of log functions already, lols…

I'm doing pretty well, what textbook are you guys using? The BC and AB classes use the same textbook here, I dont know if it's standard

That would make sense because integral is also known as anti-derivative, and because the derivative of ln(x) is 1/x, the integral of 1/x is ln(x) + c where c is a constant.

Also integral is the area under a graph.

yeah i konw all that… but we used that definition to prove the derivative tho

i dont UNDERSTAND why tho, like what is the relation to the other definition of ln (log base e)

we are doing stuff in a different order, but i gues it works since lsat year 80% of the class got 5s

we did a bunch of summation stuff and anti-derivative stuff, and spent a bunch of time proving the fundamental theorem of calculus and multiplication rule, chain rule, all that stuff

so ……. you want to know what e is? Because i didn't understand one word.

From: Macrosoft
my mind was blown yesterday when my math teacher defined ln(x) as the integral from 1 to x of 1/x….can someone explain this magic??

also, e is a crazy number…

Also i was wondering how people are doing in BC Calc (if they are taking it) because the average grade on our last test was 62….

What do you mean, the integral from 1 to x of 1/x? ln|x| + c is the integral of 1/x in general.. Maybe you are thinking of this other random identity which is that the integral from 1 to e of 1/x = 1?

Hmm.. so the integral of 1/x from 1 to x is indeed ln|x| (just did it), but only if you already know that the integral of 1/x is ln|x|, it could just as easily be any function where f(1) = 0.. Seems kind of a pointless definition since it requires that you already know that the integral of 1/x is ln|x|. Did the teacher give any proof (or justification) of that this is indeed the case? What is it exactly that you are confused about?

From: any_one
What is it exactly that you are confused about?

Thats what i want to know too.

He wants to see a proof for the definition of the derivative of ln(x).

l2google.

http://math2.org/math/derivatives/more/ln.htm

http://ca.answers.yahoo.com/question/index?qid=20061108142002AAn4YGU

i was just confused as to how the two definitions of ln were related but that last post with the proof kind of helps

he wants he meaningful explanation for why it is true, not a rigorous mathematical proof that the limit reduces to said expression. something like a graphical proof, such as one for the pythagorean theorem: http://www.mathopenref.com/pythagorasproof.html

The definition

ln(x) = integral from 1 to x of 1/x

is just using the fundamental theorem of calculus which you should've already covered if you're into integrals at all

Don't gravedig, this thread is over 2 months old, and the problem is already solved, click my sig if you want help, because it looks like you need it.

From: KingKong
Don't gravedig, this thread is over 2 months old, and the problem is already solved, click my sig if you want help, because it looks like you need it.

You ought to really chill out. That's one hell of an impression you're setting about this community to a first-time poster. Keep it constructive, benefit of the doubt.

This section is pretty dead so it doesn't matter that much.

The term of grave digging is bringing back a thread 50 pages back. or 1-9999 years back.

2 months ago was not very long. And if anything threads containing information shouldn't matter if its been grave digged. I grave dig old topics too, just so the forums can have something to talk about (again).

Some of us like to grave dig threads because there may have been a question unanswered or bringing up a question that was answered.

incase you didn't know Grave digging is possibly allowed.

as NecroBumping you may be yelled at

Necrobumps

"Necrobumping" (also known as "Gravedigging"), occurs when a forum thread that has been inactive for a long time, typically years, is bumped by a reader, usually in response to what he inadvertently believes to be an ongoing discussion. Most of the time this is met with ridicule and sometimes a ban, and can be quite annoying to adept members (who are generally intolerant and dismissive of anybody who does not waste as much of their life on forums as they do).

My crappy source:

http://en.wikipedia.org/wiki/Bump_%28Internet%29