/sci/ - Science & Math » Thread #12533980

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In case it isn´t common knowledge

Anonymous Sat 02 Jan 00:06:54 2021 No.12533980 View Reply Original Report

Quoted By: >>12534134 >>12541085 >>12543964

The n-th integral of a bounded function in a finite domain converges to 0

Anonymous

Anonymous Sat 02 Jan 2021 00:26:59 No.12534035 Report

Quoted By:

bump

Anonymous

Anonymous Sat 02 Jan 2021 01:05:28 No.12534134 Report

Quoted By: >>12534150

>>12533980
>The n-th integral of a bounded function in a finite domain converges to 0

doubt

Anonymous

Anonymous Sat 02 Jan 2021 01:13:05 No.12534150 Report

Quoted By: >>12534192

>>12534134
I can do a proof for an arbitrary function f:[0,a]->R if you'd like, it can be built up from there

Anonymous

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Anonymous Sat 02 Jan 2021 01:28:25 No.12534192 Report

Quoted By: >>12534208 >>12536142 >>12540342 >>12542942

>>12534150

Anonymous

Anonymous Sat 02 Jan 2021 01:35:06 No.12534208 Report

Quoted By:

>>12534192
Then you can use shit like the linearity of the integral and stuff like that to prove the statement for all those functions $f: A \subset R \rightarrow R$ , it can be easily extended for functions $f: A \subset R^{n} \rightarrow R^{m}$

Anonymous

Anonymous Sat 02 Jan 2021 01:51:07 No.12534248 Report

Quoted By:

is this not common knowledge/ useful?

Anonymous

Anonymous Sat 02 Jan 2021 03:49:30 No.12534531 Report

Quoted By:

bump again

Anonymous

Anonymous Sat 02 Jan 2021 06:53:37 No.12534976 Report

Quoted By: >>12537930

for fucks sake /sci tell me if it's common knowledge or not, not one result of this pops up so my eager cock is throbbing with anticipation of a mediocre paper

Anonymous

Anonymous Sat 02 Jan 2021 13:11:08 No.12536142 Report

Quoted By: >>12537320

>>12534192
What about e^x?

Anonymous

Anonymous Sat 02 Jan 2021 13:15:36 No.12536149 Report

Quoted By: >>12537320

Um
f(x)=sin(x)?

Anonymous

Anonymous Sat 02 Jan 2021 13:18:52 No.12536157 Report

Quoted By:

Based schizo retard

Anonymous

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Anonymous Sat 02 Jan 2021 20:22:08 No.12537320 Report

Quoted By:

>>12536142
See pic related for proof, you're not taking into consideration the constant given by the lower bound.

>>12536149
Proof is analogous to pic related

Anonymous

Anonymous Sat 02 Jan 2021 22:49:04 No.12537897 Report

Quoted By:

bumperino

Anonymous

Anonymous Sat 02 Jan 2021 22:55:21 No.12537930 Report

Quoted By: >>12537991

>>12534976
you could maybe have a footnote about this in a slide for a larger project or something, but for sure not a paper.

Anonymous

Anonymous Sat 02 Jan 2021 23:08:12 No.12537991 Report

Quoted By:

>>12537930
Anything that fills up space is as good as anything anon, thanks

Anonymous

Anonymous Sun 03 Jan 2021 15:35:47 No.12540342 Report

Quoted By: >>12542538

>>12534192
we don't know that f greater or equal than 0 only that the absolute value of f is greater or equal to some c. just erase the "0 <=" part and say the rest is analog

Anonymous

Anonymous Sun 03 Jan 2021 19:59:51 No.12541085 Report

Quoted By: >>12542538

>>12533980
Can you explain what you mean by ""the"" n-th integral of a function? Do you mean the n-dimensional space of functions whose n-th derivative is the original function?

Anonymous

Anonymous Mon 04 Jan 2021 02:54:48 No.12542538 Report

Quoted By: >>12543602

>>12540342
thanks anon, will do

>>12541085
Yes. I just realized this follows trivially from cauchy formula for iterated integration in R. However, even though I couldn´t get a formula for iterated integration in R^n I could prove that it's end behaviour is pretty much the same .

Anonymous

Anonymous Mon 04 Jan 2021 05:45:56 No.12542942 Report

Quoted By: >>12543140

>>12534192
I like your textbook handwriting

Anonymous

Anonymous Mon 04 Jan 2021 07:18:49 No.12543140 Report

Quoted By:

>>12542942
thanks anon, i try my best. The limits might look a bit shitty but I guess that's just the way it is after months of writing the little shits.

Anonymous

Anonymous Mon 04 Jan 2021 11:25:13 No.12543602 Report

Quoted By: >>12545428

>>12542538
So can you explain what you mean by the n-th integral?

Anonymous

Anonymous Mon 04 Jan 2021 14:26:54 No.12543964 Report

Quoted By: >>12545428

>>12533980

How are you fuckers always reading my thoughts?

I spent the last few days thinking of a clearer train of discovery for Taylor series, and I settled on the weighted mean value theorem (for integration) and the convergence of iterated integration an arbitrarily large number of times.

Anonymous

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Anonymous Mon 04 Jan 2021 22:40:44 No.12545428 Report

Quoted By:

>>12543602
Pic related

>>12543964
Kek anon two weeks ago I made a formula for integration using imtegration by parts n times and thought I had made something big, then I googled the statement and realized I had gotten to the general taylor series theorem for integration. Feels bad man.

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