/sci/ - Science & Math » Thread #14005639

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Anonymous Fri 24 Dec 18:52:38 2021 No.14005639 View Reply Original Report

Quoted By: >>14005665 >>14005709 >>14005821 >>14006283 >>14007057 >>14007096 >>14008233 >>14013121

whenever I see this symbol in a paper I shit my pants in fear

Anonymous

Anonymous Fri 24 Dec 2021 18:54:35 No.14005645 Report

Quoted By:

It looks snaky, doesn't it?

Anonymous

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Anonymous Fri 24 Dec 2021 19:00:15 No.14005662 Report

Quoted By:

AHHHHH I'M GOING INSANE

[fortune color="#01aad0"]Your fortune: You got an extra thick slice of fruitcake.[/fortune]

Anonymous

Anonymous Fri 24 Dec 2021 19:00:58 No.14005665 Report

Quoted By: >>14007619

>>14005639
Don't read old books with the long S then

Anonymous

Anonymous Fri 24 Dec 2021 19:11:00 No.14005709 Report

Quoted By:

>>14005639
$\int ummation$

Anonymous

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Anonymous Fri 24 Dec 2021 19:30:04 No.14005763 Report

Quoted By: >>14005766 >>14005777 >>14005795 >>14005814 >>14008500

can someone help me out with this one?

Anonymous

Anonymous Fri 24 Dec 2021 19:30:44 No.14005766 Report

Quoted By:

>>14005763
me on the right

Anonymous

Anonymous Fri 24 Dec 2021 19:33:48 No.14005777 Report

Quoted By:

>>14005763
just differentiate both sides

Anonymous

Anonymous Fri 24 Dec 2021 19:36:40 No.14005791 Report

Quoted By:

oh come on
don't let the mathematicians intimidate you

Anonymous

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Anonymous Fri 24 Dec 2021 19:38:20 No.14005795 Report

Quoted By:

>>14005763
P A R S E
E R R O R

Anonymous

Anonymous Fri 24 Dec 2021 19:43:11 No.14005814 Report

Quoted By:

>>14005763
use of oo or ? is not standard
textbooks have different explanations
different authors use it in different ways
so the answer will be "infinity" or "undefined" depending on context
without context, it is neither of these

Anonymous

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Anonymous Fri 24 Dec 2021 19:44:05 No.14005821 Report

Quoted By:

>>14005639
fuck you for posting this on christmas

Anonymous

Anonymous Fri 24 Dec 2021 20:01:53 No.14005876 Report

Quoted By: >>14005894 >>14005903 >>14005904 >>14007057

can someone give the definition of "indefinite integral"?

Anonymous

Anonymous Fri 24 Dec 2021 20:08:44 No.14005894 Report

Quoted By: >>14005909 >>14005910 >>14007057 >>14013064

>>14005876
An indefinite integral is a function such that if differentiated becomes the original function, so that x^2 - 4 is an indefinite integral of 2x.

Anonymous

Anonymous Fri 24 Dec 2021 20:10:27 No.14005903 Report

Quoted By: >>14005909 >>14006293

>>14005876
American English for a primitive function.

Anonymous

Anonymous Fri 24 Dec 2021 20:10:29 No.14005904 Report

Quoted By: >>14005909

>>14005876
antiderivative bro

Anonymous

Anonymous Fri 24 Dec 2021 20:11:37 No.14005909 Report

Quoted By: >>14005925 >>14005927 >>14006293 >>14007057

>>14005894
>>14005903
>>14005904
so is it just one function?

Anonymous

Anonymous Fri 24 Dec 2021 20:11:37 No.14005910 Report

Quoted By: >>14005931

>>14005894
But the derivative of 2x is 2...

Anonymous

Anonymous Fri 24 Dec 2021 20:15:40 No.14005925 Report

Quoted By:

>>14005909
depends on what you mean by that but sure. the antiderivative takes a separate function as its argument but the whole thing can be viewed as one function.

Anonymous

Anonymous Fri 24 Dec 2021 20:16:16 No.14005927 Report

Quoted By:

>>14005909
Yes, but it's part of a family of other primitive functions, all equal to each other modulo constants different for each disconnected component.

Anonymous

Anonymous Fri 24 Dec 2021 20:17:11 No.14005931 Report

Quoted By: >>14006131 >>14006261

>>14005910
Yeah, that means that 2x is an indefinite integral of 2

Anonymous

Anonymous Fri 24 Dec 2021 21:13:13 No.14006131 Report

Quoted By: >>14008211

>>14005931
where does the x come from?

Anonymous

Anonymous Fri 24 Dec 2021 21:43:08 No.14006261 Report

Quoted By: >>14008211

>>14005931
you can't just put an x there what

Anonymous

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Anonymous Fri 24 Dec 2021 21:48:33 No.14006283 Report

Quoted By: >>14006289 >>14006312

>>14005639
What's wrong op?

Anonymous

Anonymous Fri 24 Dec 2021 21:50:49 No.14006289 Report

Quoted By:

>>14006283
omg pls stop

Anonymous

Anonymous Fri 24 Dec 2021 21:51:24 No.14006293 Report

Quoted By: >>14006931

>>14005903
>>14005909
No it's the set of all primitive functions.

Anonymous

Anonymous Fri 24 Dec 2021 21:56:10 No.14006312 Report

Quoted By: >>14006342 >>14006372

>>14006283
please explain strokes theorem, I need to do a presentation on it soon

Anonymous

Anonymous Fri 24 Dec 2021 22:06:45 No.14006342 Report

Quoted By: >>14006344 >>14006372

>>14006312
literally read the notation
"you are taking the integral of some function ?. You're taking this integral over a region. In this case, the region is actually just an infinitesimally small change over another function ?, $\partial \Omega$ .
It turns out that this integral of ? over $\partial \Omega$ is the exact same thing as taking the integral of some infinitesimal interval of ?, $d\omega$ , but over the entirety of the function ?."

Anonymous

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Anonymous Fri 24 Dec 2021 22:07:44 No.14006343 Report

Quoted By:

I hate coends too!

Anonymous

Anonymous Fri 24 Dec 2021 22:09:15 No.14006344 Report

Quoted By: >>14006348

>>14006342
>the region is actually just an infinitesimally small change over another function
lost me here

Anonymous

Anonymous Fri 24 Dec 2021 22:10:35 No.14006348 Report

Quoted By:

>>14006344
you're taking the integral over a point on another function

Anonymous

Anonymous Fri 24 Dec 2021 22:17:18 No.14006372 Report

Quoted By:

>>14006312
The integral of the exterior derivarive of a n-1 form over an n chain is equal to the integral of the n-1 form over the boundary.
Although you're probably talking about stokes theorem from vector calc, wich is a special case of the generalized version.

What the theorem essentially says is that the integral over a curve in $\mathbb{R^3}$ of the dot product of the tangent vector to the curve with a vector field, wich can be viewed as integrating the force along a distance on a particle (yielding the work done on the particle) is equal to the integral of the curl of the vector field dotted with a surface normal of a surface that has the curve as boundary.
>>14006342
Stop trolling him.

Anonymous

Anonymous Sat 25 Dec 2021 01:17:26 No.14006931 Report

Quoted By: >>14007408

>>14006293
so what's indefinite integral of 1/x?

Anonymous

Anonymous Sat 25 Dec 2021 01:57:57 No.14007057 Report

Quoted By:

>>14005639
Do you also get scared by plus signs, you pussy? Because that's what this symbol is.

>>14005876
>>14005894
>>14005909
Not one function, but a FAMILY of functions. That's what the +C is for, because you literally have infinitely many solutions to dF/dx = f.

Anonymous

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Anonymous Sat 25 Dec 2021 02:15:56 No.14007096 Report

Quoted By:

>>14005639
As the paper on the left shows, integral symbols
make even the trickiest of calculations look smooth
and distinguished.

There is literally nothing to worry about...

Unless an area under a set of fractal stairs over
a union of disjoint sets scares you, then you
should come to terms with what an integral
is very quickly.

Anonymous

Anonymous Sat 25 Dec 2021 04:28:02 No.14007408 Report

Quoted By: >>14008211

>>14006931
The set of functions given by $\log\,\lvert x\rvert + C_1[x < 0] + C_2[x > 0]$ for each choice of $C_1,C_2\in {\bf R}$ where $[\cdot]$ is the Iverson bracket.

Anonymous

Anonymous Sat 25 Dec 2021 05:40:46 No.14007619 Report

Quoted By: >>14013361

>>14005665
It's annoying as fuck. In some books it's one of those for every first s in every word. Shit looks like f. It's hard to read, it makes me wonder why this was done.

Anonymous

Anonymous Sat 25 Dec 2021 10:42:39 No.14008211 Report

Quoted By: >>14008221

>>14006261
>>14006131
Probably troll but 2=2(x^0) so if you want to integrate that with respect to x just add one to the power and divide by the power (which is 1) so that you get 2x.

>>14007408
>absolute value
I hope you realise it's only there because high-school textbooks are scared of complex numbers, its just logx + constant

Anonymous

Anonymous Sat 25 Dec 2021 10:45:37 No.14008221 Report

Quoted By: >>14008272

>>14008211
>I hope you realise it's only there because high-school textbooks are scared of complex numbers, its just logx + constant
no. log(x) is not even a real number for negative argument.

Anonymous

Anonymous Sat 25 Dec 2021 10:49:05 No.14008233 Report

Quoted By: >>14009120

>>14005639
$\displaystyle<br />\oint_{\oint_{\oint_{\oint_{\oint_{\oint_{\oint}^{\oint}}^{\oint_{\oint}^{\oint}}}^{\oint_{\oint_{\oint}^{\oint}}^{\oint_{\oint}^{\oint}}}}^{\oint_{\oint_{\oint_{\oint}^{\oint}}^{\oint_{\oint}^{\oint}}}^{\oint_{\oint_{\oint}^{\oint}}^{\oint_{\oint}^{\oint}}}}}^{\oint_{\oint_{\oint_{\oint_{\oint}^{\oint}}^{\oint_{\oint}^{\oint}}}^{\oint_{\oint_{\oint}^{\oint}}^{\oint_{\oint}^{\oint}}}}^{\oint_{\oint_{\oint_{\oint}^{\oint}}^{\oint_{\oint}^{\oint}}}^{\oint_{\oint_{\oint}^{\oint}}^{\oint_{\oint}^{\oint}}}}}}^{\oint_{\oint_{\oint_{\oint_{\oint_{\oint}^{\oint}}^{\oint_{\oint}^{\oint}}}^{\oint_{\oint_{\oint}^{\oint}}^{\oint_{\oint}^{\oint}}}}^{\oint_{\oint_{\oint_{\oint}^{\oint}}^{\oint_{\oint}^{\oint}}}^{\oint_{\oint_{\oint}^{\oint}}^{\oint_{\oint}^{\oint}}}}}^{\oint_{\oint_{\oint_{\oint_{\oint}^{\oint}}^{\oint_{\oint}^{\oint}}}^{\oint_{\oint_{\oint}^{\oint}}^{\oint_{\oint}^{\oint}}}}^{\oint_{\oint_{\oint_{\oint}^{\oint}}^{\oint_{\oint}^{\oint}}}^{\oint_{\oint_{\oint}^{\oint}}^{\oint_{\oint}^{\oint}}}}}}<br />$

Anonymous

Anonymous Sat 25 Dec 2021 10:57:58 No.14008272 Report

Quoted By: >>14008599

>>14008221
It doesn't have to be.
If you're contending that this means that it no longer represents the area of 1/x for negative x then this is fine also as the integral is not formally defined as an area function, only the function that when differentiated yields the parent function. This also implicitly states that logx and log|x| have different derivatives, which is not true.

Anonymous

Anonymous Sat 25 Dec 2021 11:35:45 No.14008500 Report

Quoted By: >>14013324

>>14005763
$\int{e^{x}}\mathrm{d}x = e^{x} + C$

elementary integral

Anonymous

Anonymous Sat 25 Dec 2021 11:46:37 No.14008599 Report

Quoted By: >>14008634 >>14013311

>>14008272
can you provide the exact definition of the indefinite integral of a function f : U -> R where U is some subset of R?

Anonymous

Anonymous Sat 25 Dec 2021 11:49:41 No.14008634 Report

Quoted By:

>>14008599
yes nigger its the area under the curve of f with f taking values from U and mapping them onto R

Anonymous

Anonymous Sat 25 Dec 2021 12:21:22 No.14009120 Report

Quoted By: >>14009426

>>14008233
how much time have you spent typing this out?

Anonymous

Anonymous Sat 25 Dec 2021 12:33:22 No.14009426 Report

Quoted By:

>>14009120
He obviously just generated it programmatically.

Anonymous

Anonymous Sun 26 Dec 2021 00:31:32 No.14013064 Report

Quoted By:

>>14005894
Indefinite integrals span the entire area of the function

Definite integrals concern themselves with a specific range of values under the function’s curve

Anonymous

Anonymous Sun 26 Dec 2021 00:48:48 No.14013121 Report

Quoted By:

>>14005639
If you integrate and shit your pants then you should be able to differentiate the shit back into your ass

Anonymous

Anonymous Sun 26 Dec 2021 01:43:33 No.14013311 Report

Quoted By: >>14013380

>>14008599
>f : U -> R
What does this notation say in plain English?
Function f something U to R?

Anonymous

Anonymous Sun 26 Dec 2021 01:49:41 No.14013324 Report

Quoted By: >>14013350 >>14013392

>>14008500
Where does the C come from?

Anonymous

Anonymous Sun 26 Dec 2021 01:57:14 No.14013350 Report

Quoted By:

>>14013324
hell

Anonymous

Anonymous Sun 26 Dec 2021 01:59:55 No.14013361 Report

Quoted By:

>>14007619
To filter illiterates like you.

Anonymous

Anonymous Sun 26 Dec 2021 02:04:50 No.14013380 Report

Quoted By:

>>14013311
function which maps the elements of set U to set R

Anonymous

Anonymous Sun 26 Dec 2021 02:07:06 No.14013392 Report

Quoted By:

>>14013324
differentiate functions e^x+2 e^x+3 e^x-pi functions

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