Author Topic: integral of......  (Read 3422 times)

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Offline Kosh

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ln(tan(x)) dx


I'm not even sure where to start with this. Anyone got some pointers so I can get going on it? Thanks.
"The reason for this is that the original Fortran got so convoluted and extensive (10's of millions of lines of code) that no-one can actually figure out how it works, there's a massive project going on to decode the original Fortran and write a more modern system, but until then, the UK communication network is actually relying heavily on 35 year old Fortran that nobody understands." - Flipside

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Offline redsniper

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Well, you'll have to use the Chain Rule, I'm pretty sure.
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Offline Kosh

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the chain rule is for derivatives, this is an integration problem.
"The reason for this is that the original Fortran got so convoluted and extensive (10's of millions of lines of code) that no-one can actually figure out how it works, there's a massive project going on to decode the original Fortran and write a more modern system, but until then, the UK communication network is actually relying heavily on 35 year old Fortran that nobody understands." - Flipside

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STRONGTEA. Why can't the x86 be sane?

 

Offline ssmit132

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We just did integrals in our final Maths B test...

...but that was only with Logs of base 10. What is this for, exactly?

  

Offline CP5670

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You can't express this in terms of elementary functions. There are various additional, standard functions that allow you to write things like this in closed form. My guess is it would involve a polylog or Lerch function somewhere, just from looking at it.

 
We just did integrals in our final Maths B test...

...but that was only with Logs of base 10. What is this for, exactly?

You sure it wasn't base e - these are much easier.

It's been too long since my last maths units....
STRONGTEA. Why can't the x86 be sane?

 

Offline ssmit132

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No, we did logs of base 10. Although we just did simple stuff. Like log xn = n log x and so forth. And most of the time on the calculator. We haven't done ln (base e) yet. Knowing some of the people in my class, I'm sure they had trouble with these logs, which, on our scientific calculators, can ONLY do base 10 logs.  ;)

This is Maths B in Queensland, and we haven't got a good reputation when it comes to smartness IIRC.  :hopping:

 
Just wait 'til you see the new WA curriculum  :)

I thought you meant integrals of log10


Don't forget that ln x = log(x)/log(e)... Which scientific calculator do you have?

Keep up the good work - I'm originally from Queensland!
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Offline ssmit132

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A Casio fx-82MS.

And thank you, the same to you!

 

Offline Kosh

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We just did integrals in our final Maths B test...

...but that was only with Logs of base 10. What is this for, exactly?

Calculus homework, and it isn't log(tanx), it's ln(tanx).
"The reason for this is that the original Fortran got so convoluted and extensive (10's of millions of lines of code) that no-one can actually figure out how it works, there's a massive project going on to decode the original Fortran and write a more modern system, but until then, the UK communication network is actually relying heavily on 35 year old Fortran that nobody understands." - Flipside

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That's still just as ugly. Mathematica uses Log to mean the natural logarithm (as opposed to using ln(x)). Still Ugly.
STRONGTEA. Why can't the x86 be sane?

 

Offline Kosh

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yeah I know....   :doubt:
"The reason for this is that the original Fortran got so convoluted and extensive (10's of millions of lines of code) that no-one can actually figure out how it works, there's a massive project going on to decode the original Fortran and write a more modern system, but until then, the UK communication network is actually relying heavily on 35 year old Fortran that nobody understands." - Flipside

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I think you'd have to use integration by parts, not sure though.

 

Offline Jeff Vader

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Undoubtedly, but even then that thing is a *****. Hopefully solving that problem is not a requirement for passing the course.
23:40 < achillion > EveningTea: ass
23:40 < achillion > wait no
23:40 < achillion > evilbagel: ass
23:40 < EveningTea > ?
23:40 < achillion > 2-letter tab complete failure

14:08 < achillion > there's too much talk of butts and dongs in here
14:08 < achillion > the level of discourse has really plummeted
14:08 < achillion > Let's talk about politics instead
14:08 <@The_E > butts and dongs are part of #hard-light's brand now
14:08 <@The_E > well
14:08 <@The_E > EvilBagel's brand, at least

01:06 < T-Rog > welp
01:07 < T-Rog > I've got to take some very strong antibiotics
01:07 < achillion > penis infection?
01:08 < T-Rog > Chlamydia
01:08 < achillion > O.o
01:09 < achillion > well
01:09 < achillion > I guess that happens
01:09 < T-Rog > at least it's curable
01:09 < achillion > yeah
01:10 < T-Rog > I take it you weren't actually expecting it to be a penis infection
01:10 < achillion > I was not

14:04 < achillion > Sometimes the way to simplify is to just have a habit and not think about it too much
14:05 < achillion > until stuff explodes
14:05 < achillion > then you start thinking about it

22:16 < T-Rog > I don't know how my gf would feel about Jewish conspiracy porn

15:41 <-INFO > EveningTea [[email protected]] has joined #hard-light
15:47 < EvilBagel> butt
15:51 < Achillion> yes
15:53 <-INFO > EveningTea [[email protected]] has quit [Quit: http://www.mibbit.com ajax IRC Client]

18:53 < Achillion> Dicks are fun

21:41 < MatthTheGeek> you can't spell assassin without two asses

20:05 < sigtau> i'm mining titcoins from now on

00:31 < oldlaptop> Drunken antisocial educated freezing hicks with good Internet == Finland stereotype

11:46 <-INFO > Kobrar [[email protected]] has joined #hard-light
11:50 < achtung> Surely you've heard of DVDA
11:50 < achtung> Double Vaginal Double ANal
11:51 < Kobrar> ...
11:51 <-INFO > Kobrar [[email protected]] has left #hard-light []

 
Integration by parts isn't suitable for this question since you've got f(g(x)), not f(x)g'(x).

I think CP5670 summed it up best:
You can't express this in terms of elementary functions. There are various additional, standard functions that allow you to write things like this in closed form. My guess is it would involve a polylog or Lerch function somewhere, just from looking at it.

I've got no idea what he's on about (I really haven't done enough maths... and I can't remember all of it), but mathematica seems to spit out an answer along those lines (you gotta trust somebody :p)
Agreed with hoping that that's not a requirement for your course.
STRONGTEA. Why can't the x86 be sane?

 

Offline Jeff Vader

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Integration by parts isn't suitable for this question since you've got f(g(x)), not f(x)g'(x).
Whoops. Correct you are. Pardon our confusion.

Edit: Hmm. I consulted The Holy BookTM and started to work on the following (if I'm spewing out lies, hit me with a stick or something). If we have g(f(x)), deriving it would be Dg(f(x)) = g'(f(x))f'(x). From there, we could extrapolate that

g(f(x)) = ∫ g ' (f(x)) f ' (x) dx

, where f(x) = tan(x) and g(x) = lnx. That way we'd get

ln(tan(x)) = ∫(1 / tanx) * (1 + tan2(x))dx

or something. Brainfreeze.


Edit: Damn, ignore that. Dunno what I was thinking.
« Last Edit: December 16, 2008, 08:59:07 am by Lobo »
23:40 < achillion > EveningTea: ass
23:40 < achillion > wait no
23:40 < achillion > evilbagel: ass
23:40 < EveningTea > ?
23:40 < achillion > 2-letter tab complete failure

14:08 < achillion > there's too much talk of butts and dongs in here
14:08 < achillion > the level of discourse has really plummeted
14:08 < achillion > Let's talk about politics instead
14:08 <@The_E > butts and dongs are part of #hard-light's brand now
14:08 <@The_E > well
14:08 <@The_E > EvilBagel's brand, at least

01:06 < T-Rog > welp
01:07 < T-Rog > I've got to take some very strong antibiotics
01:07 < achillion > penis infection?
01:08 < T-Rog > Chlamydia
01:08 < achillion > O.o
01:09 < achillion > well
01:09 < achillion > I guess that happens
01:09 < T-Rog > at least it's curable
01:09 < achillion > yeah
01:10 < T-Rog > I take it you weren't actually expecting it to be a penis infection
01:10 < achillion > I was not

14:04 < achillion > Sometimes the way to simplify is to just have a habit and not think about it too much
14:05 < achillion > until stuff explodes
14:05 < achillion > then you start thinking about it

22:16 < T-Rog > I don't know how my gf would feel about Jewish conspiracy porn

15:41 <-INFO > EveningTea [[email protected]] has joined #hard-light
15:47 < EvilBagel> butt
15:51 < Achillion> yes
15:53 <-INFO > EveningTea [[email protected]] has quit [Quit: http://www.mibbit.com ajax IRC Client]

18:53 < Achillion> Dicks are fun

21:41 < MatthTheGeek> you can't spell assassin without two asses

20:05 < sigtau> i'm mining titcoins from now on

00:31 < oldlaptop> Drunken antisocial educated freezing hicks with good Internet == Finland stereotype

11:46 <-INFO > Kobrar [[email protected]] has joined #hard-light
11:50 < achtung> Surely you've heard of DVDA
11:50 < achtung> Double Vaginal Double ANal
11:51 < Kobrar> ...
11:51 <-INFO > Kobrar [[email protected]] has left #hard-light []

 
Integration by parts IS suitable here, I think.

What I meant is that (ln(tanx)) is the f(x), and you have to introduce a g'(x) equal to 1. Then start integrating by parts.

 

Offline redsniper

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Skip it.
"Think about nice things not unhappy things.
The future makes happy, if you make it yourself.
No war; think about happy things."   -WouterSmitssm

Hard Light Productions:
"...this conversation is pointlessly confrontational."

 

Offline CP5670

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Are you supposed to find the value of this integral in some interval or actually get an antiderivative? I'm guessing it's the former, since as I said earlier the latter cannot be done using only elementary functions.

Quote
That's still just as ugly. Mathematica uses Log to mean the natural logarithm (as opposed to using ln(x)). Still Ugly.

It's conventionally written as log in pretty much all math beyond the elementary level. They only differ by a constant factor anyway.

Quote
I've got no idea what he's on about (I really haven't done enough maths... and I can't remember all of it), but mathematica seems to spit out an answer along those lines (you gotta trust somebody )

Yeah, I just put it in there and it does involve a polylog as I expected. This is the thing I am referring to.

This is one of numerous "special functions" that can't be expressed using the standard, elementary functions. They come up a lot in various places though and are useful enough to be considered as basic objects in themselves.
« Last Edit: December 16, 2008, 11:44:56 am by CP5670 »