/sci/ - Science & Math » Thread #14370210

81KiB, 1366x768, OPISCORRECT.png

View Same Google iqdb SauceNAO

Proof That The Integral of the Reciprocal of x with Respect to x From -1 to -1 is 0

Anonymous Wed 06 Apr 22:28:38 2022 No.14370210 View Reply Original Report

Quoted By: >>14370841 >>14370846 >>14371419 >>14372383 >>14374308 >>14374328

Here roof that $\int_{-1}^{1}\frac{1}{x}dx=0$ See Picrel. Each side cancels out — and even the negative infinity cancels out with the positive infinity. Seriously though, I don't even know how this isn't obvious. Can you faggots just not visualise? Soulless as fuck...

Anonymous

Anonymous Thu 07 Apr 2022 00:17:42 No.14370563 Report

Quoted By: >>14370626

>>14370537
Nice try but that's a complete non-sequitur. Look at the problem again, that is what we're solving.

Anonymous

Anonymous Thu 07 Apr 2022 00:25:33 No.14370592 Report

Quoted By: >>14370724

>>14370491
>When?
Scroll up.
>Who said it was?
You needed a reminder.

Anonymous

Anonymous Thu 07 Apr 2022 00:33:18 No.14370626 Report

Quoted By: >>14370724

>>14370563
>Look at the problem again, that is what we're solving.
Yes. I'm looking. Now look here >>14370420
So can you do it? It is required to compute the integral over [-1,1] afterall.

Anonymous

Anonymous Thu 07 Apr 2022 00:42:42 No.14370654 Report

Quoted By: >>14370724

>>14370491
>okay? what does this have to do with anything?
you asked for spivak retard

Anonymous

Anonymous Thu 07 Apr 2022 00:48:32 No.14370672 Report

Quoted By: >>14370720

>>14370543
I know it actually doesn't have an answer, I'm just saying its retarded, Its a rigid function with two values of equal magnitude but opposite direction, sometimes calculus is juts plain retarded

Anonymous

Anonymous Thu 07 Apr 2022 01:09:53 No.14370720 Report

Quoted By: >>14370752

>>14370672
Which is why you can still assign some kind of number to it...despite the Reimann integral definitely not existing. Rigor fucking matters, bitch.
Btw the word you're looking for is "odd function." 1/x is an odd function, anon, and integrals of odd functions over an interval central at the origin often disappear. This isn't hidden fucking knowledge or anything.

Anonymous

Anonymous Thu 07 Apr 2022 01:10:58 No.14370724 Report

Quoted By: >>14370726 >>14370729 >>14371979

>>14370654
I asked you to read Spivak for yourself, not for me. You're the one who needs help.
>>14370592
Point to the posts.
>>14370626
Are you really going to be this fucking disingenuous? both integrals (-1 to 0 and 0 to 1) are equal, and since $a-a=0$, that's what the integral is equal to. You are literally arguing this basic ass math.
He literally defined the value of an integral in a special case and I'm doing the same. All of these definitions work because they agree with what we see. Either you really and truly don't understand mathematics or your being disingenuous, I'm sorry.

Anonymous

Anonymous Thu 07 Apr 2022 01:11:36 No.14370726 Report

Quoted By: >>14370740

>>14370724
>I asked you to read Spivak for yourself, not for me. You're the one who needs help.
you don't even know what's in spivak LMAO
>both integrals (-1 to 0 and 0 to 1) are equal
to what? show me

Anonymous

Anonymous Thu 07 Apr 2022 01:12:48 No.14370729 Report

Quoted By: >>14370740

>>14370724
>1/x is odd so it equal 0!!!!
the entire depth of your argument, basically

Anonymous

Anonymous Thu 07 Apr 2022 01:17:52 No.14370740 Report

Quoted By: >>14370853

>>14370726
> if a = b, then a-b=0.
> NoooOOoOOoOO!!1!!11! This makes no sense! I want determinant values! what are they equal to!!1!!1
I could tell you they're both equal to 2 or 4 or 2400, but it doesn't matter because that's not why their difference is zero.
>>14370729
Actually no, the entire depth of my argument is that a-a=0, which is a whole lot simpler, but hey, sometimes math is simple, anon. No need to make it complicated if you don't need to.

Anonymous

Anonymous Thu 07 Apr 2022 01:22:11 No.14370752 Report

Quoted By:

>>14370720
mate calm down, your freak out isn't impressing anybody

Anonymous

View Same Google iqdb SauceNAO 230.jpg, 16KiB, 490x586

Anonymous Thu 07 Apr 2022 01:32:54 No.14370779 Report

Quoted By:

>>14370221
>>14370239
Visualizing is too hard, do you have a proof for that?

Anonymous

Anonymous Thu 07 Apr 2022 01:55:10 No.14370841 Report

Quoted By:

>>14370210
Brother, are you a retard?

Anonymous

Anonymous Thu 07 Apr 2022 01:58:10 No.14370846 Report

Quoted By:

>>14370210
No Riemann sums exist for that integral though

Anonymous

Anonymous Thu 07 Apr 2022 02:05:12 No.14370853 Report

Quoted By:

>>14370740
and yet 1/x isnt integrable at 0
so you sum the integrals over the open intervals [-1,0) and (0,-1]
then you notice they dont converge
>a-a=0
no idea what this is supposed to mean

Anonymous

Anonymous Thu 07 Apr 2022 02:12:30 No.14370870 Report

Quoted By: >>14370887

>>14370420
> If the limit does not exist, we say that the improper integral is divergent

This is literally a definition not a theorem. Thou just committed a bias from authority. Give me the proof.

Anonymous

Anonymous Thu 07 Apr 2022 02:19:36 No.14370887 Report

Quoted By: >>14370918

>>14370870
>This is literally a definition not a theorem
"yes"
>Thou just committed a bias from authority. Give me the proof
holy fuck read a book sometime

Anonymous

Anonymous Thu 07 Apr 2022 02:32:30 No.14370918 Report

Quoted By: >>14370936

>>14370887
So you don't have a proof? So you just parrot your professor?

I think if you literally showed the proof why it's divergent, OP would shut up, and I'm genuinely curious why it is the case.

Anonymous

Anonymous Thu 07 Apr 2022 02:40:20 No.14370936 Report

Quoted By: >>14370942

>>14370918
No, I parroted a definition from a wildly popular analysis text. some other faggot ITT actually picked the author for me while trying to own the libs.
the author doesnt matter, all normal books approach improper integrals in exactly this way. have you ever read a calculus text in your entire life?

Anonymous

Anonymous Thu 07 Apr 2022 02:44:52 No.14370942 Report

Quoted By: >>14370947

>>14370936
> wildly popular analysis text
Doesn't change a thing. What is the motive?

Anonymous

Anonymous Thu 07 Apr 2022 02:46:47 No.14370947 Report

Quoted By: >>14370970

>>14370942
to develop real analysis, presumably. LOL?

Anonymous

Anonymous Thu 07 Apr 2022 02:55:19 No.14370970 Report

Quoted By: >>14370973

>>14370947
Unless I am missing something, that seems like circular logic. And in this context it's hypocritical because it's basically "proof by looking" which is why it isn't a theorem but a definition

Anonymous

Anonymous Thu 07 Apr 2022 02:57:20 No.14370973 Report

Quoted By: >>14370979

>>14370970
>Unless I am missing something
a brain

Anonymous

View Same Google iqdb SauceNAO image_2022-04-07_045925916.png, 333KiB, 2560x1919

Anonymous Thu 07 Apr 2022 02:59:45 No.14370979 Report

Quoted By: >>14370981

>>14370973

Anonymous

Anonymous Thu 07 Apr 2022 03:00:42 No.14370981 Report

Quoted By: >>14370984

>>14370979
the point is already so far beyond your comprehension, it doesnt even matter. its funny to laugh at your goofy ass.

Anonymous

Anonymous Thu 07 Apr 2022 03:00:56 No.14370983 Report

Quoted By:

$\int_{-1}^{1} \frac{dx}{x} = \lim_{a \to 0} \left[\int_{-1}^{a}\frac{dx}{x} + \int_{a}^{1} \frac{dx}{x}\right] = \lim_{a \to 0} \left[\ln |a| - 1 + 1 - \ln|a|\right] = 0$

Seriously, there is nothing complicated about this.

Anonymous

Anonymous Thu 07 Apr 2022 03:01:54 No.14370984 Report

Quoted By:

>>14370981
if you call parroting comprehension..
¯\_(?)_/¯

Anonymous

Anonymous Thu 07 Apr 2022 03:04:45 No.14370991 Report

Quoted By: >>14370993 >>14371046

>>14370403
>ctrl+f "cauchy"
>1 result
>no replies
bunch of fucking retards ITT

Anonymous

Anonymous Thu 07 Apr 2022 03:06:03 No.14370993 Report

Quoted By:

>>14370991
Well, two aren't. :)

Anonymous

Anonymous Thu 07 Apr 2022 03:33:51 No.14371046 Report

Quoted By:

>>14370991
The only retards are the ones who are quoting Spivak like it's the bible thinking it refutes OP. They have no sense of mathematics at all.

Anonymous

Anonymous Thu 07 Apr 2022 06:03:21 No.14371274 Report

Quoted By: >>14371379

Here's the correct answer for the morons from last thread who ignored it:
>>14370225
>>14370272

Anonymous

Anonymous Thu 07 Apr 2022 07:33:13 No.14371379 Report

Quoted By:

>>14371274
Thoughtful and correct answers are usually ignored on this shitty site.

Anonymous

Anonymous Thu 07 Apr 2022 07:59:44 No.14371419 Report

Quoted By: >>14371446

>>14370210
OP, what is 1+1-1+1-1+1-1 = ... ?

Anonymous

Anonymous Thu 07 Apr 2022 08:19:37 No.14371446 Report

Quoted By: >>14371451

>>14371419
1, what about it?

Anonymous

Anonymous Thu 07 Apr 2022 08:24:45 No.14371451 Report

Quoted By: >>14371454

>>14371446
why not 2?

El Arcón

El Arcón Thu 07 Apr 2022 08:27:08 No.14371453 Report

Quoted By: >>14371455

Odd function vanishes when integrated over symmetric domain.

Anonymous

Anonymous Thu 07 Apr 2022 08:27:24 No.14371454 Report

Quoted By:

>>14371451
Uh...need to go back to primary school? this is basic arithmetic.

Anonymous

Anonymous Thu 07 Apr 2022 08:28:24 No.14371455 Report

Quoted By: >>14371487 >>14371488

>>14371453
Nope, it's still there. Try again.

El Arcón

View Same Google iqdb SauceNAO TIMESAND___7BDERAUVjvtetWRTMtGHM (...).png, 27KiB, 449x509

El Arcón Thu 07 Apr 2022 09:05:30 No.14371487 Report

Quoted By:

>>14371455
What is still there?

El Arcón

View Same Google iqdb SauceNAO TIMESAND___7BDERAUVjffvtetWRTMtG (...).png, 28KiB, 461x512

El Arcón Thu 07 Apr 2022 09:07:49 No.14371488 Report

Quoted By: >>14372363 >>14373478

>>14371455
What is still there?

Anonymous

Anonymous Thu 07 Apr 2022 13:45:49 No.14371979 Report

Quoted By:

>>14370724
>Point to the posts.
Remain a brainlet.

Anonymous

Anonymous Thu 07 Apr 2022 15:30:20 No.14372212 Report

Quoted By: >>14373338

>>14370221
>what is a diagram?

Anonymous

Anonymous Thu 07 Apr 2022 16:50:09 No.14372359 Report

Quoted By: >>14372367

What is even the problem? You can't fix what? What are you trying to achieve? What's the goal? Is it worth it?
Mathfags sound like secret schizo club with their problems.

Anonymous

Anonymous Thu 07 Apr 2022 16:52:47 No.14372363 Report

Quoted By:

>>14371488
strictlu speaking, the limits of integration in lines 5 and 6 are NOT the same, so you shouldnt use the same epsilon. so they cannot he said to converge under normal reimann integration.

you can still produce a cauchy value of 0, but this is not the proof of that either.

Anonymous

Anonymous Thu 07 Apr 2022 16:53:49 No.14372367 Report

Quoted By:

>>14372359
>whats the goal
to put analysis on a rigorous of a base as possible
>is it worth it
yeah. do you really not find math inherently pleasant?

Anonymous

View Same Google iqdb SauceNAO 2344.png, 219KiB, 483x470

Anonymous Thu 07 Apr 2022 16:58:59 No.14372383 Report

Quoted By:

>>14370210
The outcome depends on how you go about integrating this thing, so there isn't any one value you can unambiguously assign to it, so it doesn't make sense to talk about "the value" of it. Why is that so difficult for normies to grasp?

Anonymous

Anonymous Thu 07 Apr 2022 22:23:54 No.14373338 Report

Quoted By:

>>14372212
>not a proof

Anonymous

Anonymous Thu 07 Apr 2022 23:27:58 No.14373478 Report

Quoted By:

>>14371488
>NaN minus NaN equals zero

Anonymous

Anonymous Fri 08 Apr 2022 04:14:54 No.14374308 Report

Quoted By:

>>14370210
All I know is the function f of x is equal to
x squared plus x cubed bro...

Anonymous

Anonymous Fri 08 Apr 2022 04:20:26 No.14374328 Report

Quoted By:

>>14370210
>infinity - infinity = 0 because LOOK AT THIS NECESSRY FINITE PICTURE
Haaaa....

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches