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/sci/ - Science & Math

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3188626 No.3188626 [Reply] [Original]

A surface under an area is always positive.
My math teachers say that the integral of -x^5 from 1 to 3 is -363/3, which is obviously a negative number. mathematicans say that the integral is the surface under a curve but this is an contradiction- hasn't anyone noticed that before me?

>> No.3188635

the integral of -x^5 from 1 to 3 is not under the curve though, it is above the curve and under the x axis

>> No.3188639

>>3188626
It's only the area under the curve if the function is positive in the given interval.

>> No.3188644

so I must check everytime where the x-axis is?

>> No.3188641

>mathematicans say that the integral is the surface under a curve
No, they don't. The surface a curve f(x) encloses with the x axis is <span class="math">\left|\int_a^b\mathrm dx\,|f(x)|\right|[/spoiler].

>> No.3188648

>>3188644
Every single time. In fact, I'd check again after you calculate anything, just to make sure it hasn't moved.

>> No.3188651

>>3188644

It'll work itself out if you calculate the integral properly.

>> No.3188654

>>3188651
which integral property?

>> No.3188655

if you're asked to find the integral, do it as normal, but if you have to find the area under the curve you should check whether it crosses the x axis between the limits and if so, integrate it separately between points where it crosses the axis and then add the size of each integral, if that makes sense

>> No.3188658

>>3188644
if you are after area you must check for roots of the function you will integrate, and integrate between those

>> No.3188661

>>3188651
not for area

you have to absolute value everything

>> No.3188672

>>3188661
before or after?

>> No.3188675

>>3188641
>implying you need the outer absolute value
>implying the integral of a positive quantity will be negative

>> No.3188680

>>3188675
1. For <span class="math">b<a[/spoiler] you'll need the outer abs.
2. There are negative functions. Act surprised.

>> No.3188684

The rule is that after an area phase there always is a negative area phase. If you start with a negative area phase then you wait to the area spacce, intergrate from 0 to 0 values of y on the x axis, then skip the negative area phase which is again followed by an area phase and so on. Just plot the curve before you integrate. If it's a multi-integral, then you can't figure it out beforehand in most cases

>> No.3188685

>>3188680
>implying anyone integrates over reversed intervals
>implying the inner abs doesn't take care of any negative value in the function

Keep on being retarded.

>> No.3188688

"Under the curve" is misleading. What it really means is "Between the curve and y=0"

>> No.3188691

>>3188685 nobody integrates over reversed intervals
Now that was way too obvious. Have a nice day, sir.

>>3188684 The rule is that after an area phase there always is a negative area phase.
No, <span class="math">\big(\sin(x)\big)^2[/spoiler] for example.

>> No.3188695

>>\big?

>> No.3188699

>>3188695
( \big( \Big( \bigg( \Bigg(
<span class="math">\Rightarrow[/spoiler]
<span class="math">( \big( \Big( \bigg( \Bigg([/spoiler]

>> No.3188700

so is it true that

int from a to b = - int from b to a?

>> No.3188701

>>3188700
Yes.

>> No.3188706

>>3188701

but then

int of |f(x)| from a to b = - int of |f(x)| from b to a

which means it's a negative value

>> No.3188712

>>3188706
Guess why I included the outer <span class="math">|\cdot|[/spoiler] in my first post, >>3188641

>> No.3188714

>thinks areas have to be positive
>he hasn't heard of vector areas
Laughing_whores.jpg

>> No.3188718

>vector areas
!?
(you can't explain that)

>> No.3188726

>>3188718
This. There are no vector areas. There are 2-vectors that can be interpreted as (directed) area elements if you want to rape the math that's actually behind it.

>> No.3188739

>>3188726
>never heard of vector measure

josef, there is maths outside of physics you know

>> No.3188750

>>3188739
there is also signed measure. aka "charge"

>> No.3188752

>>3188739
But he doesn't know any real physics, just math.

>> No.3188755

>>3188752
he doesn't know real math either.

yesterday he thought irrational exponents just happened out of thin air.

>> No.3188759
File: 33 KB, 500x530, InvisibleMovieExplosion..jpg [View same] [iqdb] [saucenao] [google]
3188759

what are irrational exponents?

>> No.3188760

>implying vector measure can be seen

>> No.3188761

>>3188759
>posting pics from icanhazcheesburger.com
>confirmed for newfag

>> No.3188762

>>3188759
People who express stupid points of view.

>> No.3188770

>>3188759
well 2^pi for example

>> No.3188777

>>3188755 yesterday he thought irrational exponents just happened out of thin air.
Nope, but nice try.

>signed measure
<span class="math">\mu(A)\geq0[/spoiler], isn't it?
>aka "charge"
Charge as I know it is Noether charge, which has to do with symmetry and nothing with area at all.

>But he doesn't know any real physics, just math.
>he doesn't know real math either.
>josef, there is maths outside of physics you know
Guys ... at least decide on one agenda

>> No.3188784

>>3188777
>Guys ... at least decide on one agenda

Everyone judges on what he knows. It appears that the consensus is that you don't know shit about anything.

>> No.3188785

>>3188777
Ignore the second paragraph. There actually is signed measure, and it's called charge. Mind=blown.

>> No.3188787

>>3188777
You just took our conclusion in advance:
>He knows neither math nor physics.
>He's posting on a board for stupid teenagers without friends

>> No.3188794

>>3188785
>gets proved wrong yesterday, admits it.
>today denies it.
>gets proved wrong about something new, admits it.

so amnesia tomorrow also?

>> No.3188797

>>3188777
It has if you consider area as a bound.

>> No.3188800

>>3188794
Such is the life of a tripfag. If he made a scene instead of admitting it, more people would notice. Instead, he hopes to sweep it under the rug so it doesn't ruin his "reputation".

>> No.3188804

>>3188777
>Guys ... at least decide on one agenda
you are thinking we conspire to the same conclusion, rather than come to it independently?

paranoid much.

your problem is you have that common flaw in somewhat smart people "if i haven't heard of it it is nonsense".

>> No.3188807
File: 21 KB, 702x135, sshot_2011-06-07_17:56:40.png [View same] [iqdb] [saucenao] [google]
3188807

>>3188794
You must be new here. I'm untrollable.
>>3188800
He, however, is. Me having a name is enough for that. Lovely to watch every single time.

Well, got to leave now, I need to finish my book on ancient sociology.

>> No.3188815

>>3188807
>I need to take my leave before I make an ass out of myself yet again

It's fine, you may go.

>> No.3188818

Why are you guys hating on Josef?
The more post-high school people here the better

>> No.3188822

>>3188807
What is \delta_A?

>> No.3188824

>>3188818
>The more post-high school people here the better

EK is post-HS as well. Yet the board would be much better without him.

>> No.3188828
File: 40 KB, 703x226, sshot_2011-06-07_18:11:24.png [View same] [iqdb] [saucenao] [google]
3188828

>>3188822 What is \delta_A?
Codifferential operator, pic related

>> No.3188834

>>3188828
>>3188807

Aus welchem Buch / Skript sind diese Definitionen?

>> No.3188841

ah okay, it's clear now

>> No.3188842

>>3188807
we were talking about how e is defined. remember now?

>> No.3188844
File: 22 KB, 425x397, sshot_2011-06-07_18:13:44.png [View same] [iqdb] [saucenao] [google]
3188844

>>3188834
Siehe Bild. Ich würde sie heiraten nur um den Namen anzunehmen haha
Das Buch gibt's bei Springerlink (oder auf meiner Platte)

>> No.3188850

>>3188818
because though he's great within his field, he is an arrogant wanker outside of it.

witness the "negative measure doesn't exist", "oh it does, because i just read it somewhere else" ITT

>> No.3188849

is there a short derivation why for example
1^i
is what it is?

>> No.3188848

>>3188842
Yes, I remember the talk, but I'm having a hard time remembering the part where I said rational exponents appeared by magic

>> No.3188852

>>3188844
what's so great about "Baum"??

>> No.3188857
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3188857

>>3188850
>he is an arrogant wanker outside of it.

last time I checked, all physicists are this way

>> No.3188859

>>3188852
It's German for "tree". And it sounds funny.
If I started marrying people for their names I'd have to wait until gay marriage is legal here and get Buhmann ("boogieman") from one of our profs as well

>> No.3188861

>>3188857
You've never met any physicists.

>> No.3188862

>>3188848
you mocked the need for a "shit load of work" to get them. then when it was pointed out that all those real analytic notions about continuity and convergence were required, said fair enough i stand corrected.

without this "i know everything within my field therefore i know everything" attitude you'd be a great trip, but you can't seem to shake it.

besides, i thought you were taking your leave.

>> No.3188864
File: 1.28 MB, 3500x2333, mfwkneiflarv.jpg [View same] [iqdb] [saucenao] [google]
3188864

>>3188859

>> No.3188867

>>3188857
no not at all. mathsfag here, i know some great physicists who don't do this.

>> No.3188871

>>3188862
>besides, i thought you were taking your leave.
That's the downside of reading PDFs on a laptop. I've got the hard copy at home, but that won't help me much right now. Meh

>you mocked the need for a "shit load of work" to get them
I didn't mock, at least I didn't intend to.

>> No.3188878

>>3188850
>because though he's great within his field, he is an arrogant wanker outside of it.

This applies to every trip in /sci/ except EK and Inurdaes, because he/she still doesn't know how a penis works and the latter's an underage retard. I'm glad they're banned.

>> No.3188881

the chapters on classification of Riemann manifolds looks really freaky

>> No.3188885

>>3188878
He never said Josef is the only one like that.

Being surrounded by assholes doesn't excuse someone for being an asshole themselves.

>> No.3188888

>>3188881
The whole book looks really freaky, it takes me forever to understand single pages, but since I don't really need it time's on my side for now

(Also lol at people complaining about assholes on 4chan)

>> No.3188892

>>3188848
>rational
think you mean irrational

>> No.3188899

>>3188892
"Arbitrary". ;-)
Anyway, gotta catch the bus. Feel free to bash on me later

>> No.3188901

>>3188888
>using existence of other assholes to justify my asshole behaviour

ethics is also outside your field, because this is an elementary error.

>> No.3188903

>>3188885
I wasn't excusing his behavior, though.