Just finished calc II.
How would you find the area bounded between these two curves? Is it possible without the aid of a computer?
>>7686538
You haven't finished calc 2 yet, go back and study
>>7686540
But these integrals don't exist in terms of elementary functions.
>>7686545
just make up some new functions to express their integrals and compute them
>>7686565
How would I achieve this?
>>7686576
Creativity my good man.
>>7686540
> stop talking about high level math on the math board
> inb4 calc II isn't high level
>>7686585
I wouldn't doubt it. But have I the appropriate mathematical methods in my possession at my current level of education? Surely you can't expect a carpenter to build a house without a few materials to work with.
>>7686587
calc 2 (meaning the elementary theory of sequences/series and Riemann-Stieljes integration) is learned at 13-14 years of age by anyone who isn't mentally disabled. Try again
>>7686587
It really isn't.
>>7686595
I really hate this side of /sci/.
These are the kinds of people that will never amount to anything.
>>7686595
well meme'd
>>7686598
Writing two papers publishing non-trivial results on an open problem in Diophantine approximation during 2nd year of undergrad doesn't sound like someone who will "never amount to anything". In fact, everyone I know who isn't a complete mathematical moron is similarly 4-5 years ahead of the standard American math curriculum.
Stop trying to bring everyone down to the mud in order to flatter yourself you mediocre zilch.
>>7686606
Did something upset you? You seem really butthurt.
Of course it's possible without the aid of computers: you just perform the same kind estimations as a computer would make only by hand and it'd take forever. But why would you want to?
Keep in mind, more often than not there's no practical way to "calculate" things like sin( 13) or 1.71356^1.71356, computers just use clever approximations. And before computers people looked up approximated values in tables and slide rules and performed simple tricks on them.
>>7686606
I'm sorry, do you think that's at all an impressive subject to boast about?
>>7686606
Casting your net wide, eh? Not a wise tactic since it makes you easier to ignore.
>>7686606
They more likely meant that no matter your outward accomplishments you'd likely remain the same broken, self limited garbage you always were. A fair assumption judging by your present attitudes.
Not sure how you would do it, but WolframAlpha could.
>>7686612
No, it's a pretty lenient standard for people who want to be involved in mathematics in their careers. If you're boasting about what should b 14 year old American "calc 2" as being advanced math then your standards are in the toilet and I'm helping you see how low you've fallen
>>7686619
Look dude, no one here thinks Calc 2 is "advanced" maths. However, saying that anyone who didn't learn it when they were 13 is retarded is a bit much.
>>7686590
>I wouldn't doubt it. But have I the appropriate mathematical methods in my possession at my current level of education?
I'm just memeing at you. I don't know how to integrate those and I have an MS in math, though I don't study analysis.
>>7686619
Listen, man, you small, small, little man
That was my first post in this thread, I'm not claiming anything here. I'm an undergrad who's published an actual independently discovered theorem with its proof, so cool your little hot-shot jets. Why are you so angry and hateful? Like some serious stuff must be going down or must have gone down in your life if the only way you can get your own self-validation is by belittling others on an anonymous board. Do you need someone to talk to? Like, what's up dude?
>>7686633
>Listen, man, you small, small, little man
???
>>7686606
So you're fluent in the language of physical nature. Congratulations. Be humble; as anyone who truly understands math would be humbled by the notion. No need act like an ass.
>>7686633
Any civilized country can teach 14 year olds calculus. In fact we were taught basic theory of group transformations and for example the discriminant of the quadratic and cubic polynomial via the field-norm in a splitting field, in middle school. Don't get mad when I point out that you're 4-5 years behind.
>>7686647
In which mighty microman fails elementary reading comprehension
>>7686647
>we were taught basic theory of group transformations and for example the discriminant of the quadratic and cubic polynomial via the field-norm in a splitting field, in middle school
Holy shit. I learned like division and shit in middle school.
Where you from, man?
>>7686613
apparently not
>>7686538
Lay a bunch of rectangles over the graph and call it an approximation
>>7686670
Guess he was using the right bait.
>>7686647
They waited until middle school to teach you that basic shit?
What shithole are you from? Galois theory and all the classical field theory results were taught in third grade (I was a little slow).
>everyone claims to be published
>no one posts their "original theorems" so the high schoolers here can reproduce the proofs in 15 minutes
>>7686699
kinda bucks out the whole anonymity thing, doesn't it mate?
>>7686730
Well here's my theorem.
[eqn]\sum_{n \in \mathbb{N}} n = \frac{e^{i\pi}}{11.9999...}[/eqn]
>>7686741
not using [math]e^{\frac{i\tau}{2}}[/math]
You get the are below the blue line and subtract the area below the orange one, I think it's like that...
>>7686538
I would see what the Taylor or Fourier series representations of the functions are, and see if I could integrate those.
You would probably have to use power series to create reasonable estimates for the functions over the desired interval, then simply integrate the estimates
by logging x^x turning it into x*lnx
I'd log the other as well
try to find integrals of those
>>7686806
Faggot, look at the post right above yours
>>7686538
You can't calculate those areas directly in terms of elementary functions unless there is some really obscure trick in doing so. The only obvious route you have to calculate the area are estimations such as Riemann Sums or finding the Taylor Series for each function and integrating those.
>>7686765
You should be right, but how would you do that?
>>7686942
Taylor serieeeessssssssssssss
>>7686982
Taylor doesn't work for x^x, you'd have to use Puiseux Series
>>7687021
Only Maclaurin doesn't work. Center it at a positive value and you're fine.
I might be failing calc2 but at least I knew you needed to use mcluren/Taylor series here.
a double integral?
>>7686696
Kek, you must have been in the special ed class, we were working on connections between string theory and the langlands program in 3rd grade
if you plot x, x^x, x^x^x, x^x^x^x ad infinitum it seems that both branches converge asymptotically to the left side and meet at around x=0.0625
is the area between the y-axis and both branches non-zero or does it just converge very slowly?
what is the area?
where do the two branches meet?
where is the meeting point
>>7686759
>being a fag
>>7687211
I don't know the answer, but I like you
>>7687211
>Maple
>>7687211
plot W(-ln(x))/-ln(x) and see how it behaves around that region
post results cause i'm curious too
>>7686647
>Don't be mad that my parents could afford to send me to private school, it's your fault for picking the wrong parents.
>>7686595
>hurr durrrrr I learned this at 13
>Now at 23 I shitpost in a Hungarian homosexual forum
Jeez seem like you wasted your potential, faggot.
>>7687445
>I am good at X
>no applications
>not rich
>has not invented/revolutionized anything
>not beautiful
>not incredible in any impressive way
>literally fucking autistic
OOOOOOOOOOKAY
>>7687211
it kinda looks like a vagina, coo.
OP I have good news for you, although since I don't know how to type latex on 4chan ur fukt, cause I found a closed form. Oh well.
>>7687469
Could you explain what a closed form is please?
>>7686759
This is the content of my second paper. You must be another prodigy!
>>7687470
Yeah a closed form just an arbitrary bullshit where you say "This algorithm is specified in terms of other algorithms that seem less scary to you but are really just as bullshit" for example, pi, e, ln x, sqrt(x), sin(x) are all closed form but for the most part not exactly evaluated except for special values and are no better than Hermite or Bessel functions.
>>7687211
Can someone evaluate
[math]\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{...}}}[/math]
because I remember it being cool.
>>7687479
x=a^a^a^...
raise both sides as exponents on a:
a^x=a^a^a^...
The right side isn't changed cause it's the magic of infinity, so it's the same:
a^x=a
Apply Lambert log here googoogoogo
http://mathb.in/47442
Just count the number of squares...
Use grijalva theorem
>>7686617
you can very easily solve this integral using the trapezoidal method.
i just whipped up a matlab script to do it
integral1 =
0.7834
integral2 =
0.5731
total_int =
0.2103
>>7687297
should i look up whether LambertW is part of numpy or rather how to do loops in Maple?
Or i could be lazy, yeah lets go with that
>>7686590
You can use one of dozens of interpolation techniques to express the functions by a reasonable polynomial function.
Doing it by hand is probably too annoying and not worth the effort.
Lebesgue integration might also give a better hint, but it's been years since I've taken or had to use measure theory.
>>7686595
If only, kids definitely could if education wasn't mainly based on the Prussian system to gain obedience.
>>7686647
Middle school doesn't allow children to learn that.
You are set on a track and keep to it. Why would you suddenly jump up a few grades?
>>7686538
Is this really calc II material?
Am I missing something here or is this really as easy as it looks?
[math] P_n(x) := (1-x) \, x^n \prod_{k=0}^{n-1} \, (x+k) [/math]
[math] \int_0^1 \, x^x \, dx = \sum_{n=0}^\infty \frac{1}{n!} \int_0^1 \, P_n(x) \, dx [/math]
[math] = \frac{1}{2} + \frac{1}{12} + \frac{1}{24} + \frac{131}{5040} + \frac{1093}{60480} + ... [/math]
>>7686775
Here is your answer OP.
print it out and cut it out and weight the cutout``
>>7690909
emma stone is really beautiful
>>7691124
lol
>>7686545
Just learned in calc 3 that even if you can't take its antiderivative you can still evaluate it.
Consider the integral of that region called I.
Now consider I2 and you can perform a change of variable on the second integral and get a double integral of two variables.
Map the region I2 from rectangular coordinates to polar coordinates and you find an integral you could take an antiderivative of.
>>7691297
Supposed to be I squared.
>>7691297
and that gets you volume.
look over your notes again kid
>>7686595
My god you're a fucking moron.
I will post this here because I don't want to make a separate thread for this.
I want to know if pic related is a good book or nah?
>>7691601
As far as textbooks go:
>Go to library.
>Borrow book.
>Look through book.
>Decide if you like book.
>look through more book
>pick book you like most
With books on this level it doesn't make a difference.
