1201: "Integration by parts"

This forum is for the individual discussion thread that goes with each new comic.

Moderators: Moderators General, Prelates, Magistrates

User avatar
Quicksilver
Posts: 437
Joined: Wed Apr 29, 2009 6:21 am UTC

1201: "Integration by parts"

Postby Quicksilver » Fri Apr 19, 2013 4:14 am UTC

Image
http://xkcd.com/1201/
Alt Text:"If you can manage to choose u and v such that u = v = x, then the answer is just (1/2)x^2, which is easy to remember. Oh, and add a '+C' or you'll get yelled at."
It's been a while since I've done integration, but isn't the formula x^n = x^(n+1)/(n+1) + c?

TortoiseWrath
Posts: 22
Joined: Sun Feb 24, 2013 12:28 am UTC

Re: 1201: "Integration by parts"

Postby TortoiseWrath » Fri Apr 19, 2013 4:15 am UTC

*scratches head*

I'll have to let this one sink in for the next few years...

User avatar
rhomboidal
Posts: 797
Joined: Wed Jun 15, 2011 5:25 pm UTC
Contact:

Re: 1201: "Integration by parts"

Postby rhomboidal » Fri Apr 19, 2013 4:28 am UTC

That's practically verbatim from my high-school calc teacher.

User avatar
AluisioASG
Posts: 2337
Joined: Tue Mar 26, 2013 12:43 am UTC
Location: Flowing into places that are comfortable for it to flow
Contact:

Re: 1201: "Integration by parts"

Postby AluisioASG » Fri Apr 19, 2013 4:38 am UTC

Is this supposed to be a joke?
I don't get it (the joke part).

PS: Join us.
Selecting new quote…
Can't see addams on the right? Message me!Image

Kit.
Posts: 1117
Joined: Thu Jun 16, 2011 5:14 pm UTC

Re: 1201: "Integration by parts"

Postby Kit. » Fri Apr 19, 2013 4:43 am UTC

AluisioASG wrote:Is this supposed to be a joke?
I don't get it (the joke part).

Double meaning of "by parts".

boozledorf
Posts: 117
Joined: Mon Feb 04, 2013 6:54 am UTC

Re: 1201: "Integration by parts"

Postby boozledorf » Fri Apr 19, 2013 4:45 am UTC

Kit. wrote:
AluisioASG wrote:Is this supposed to be a joke?
I don't get it (the joke part).

Double meaning of "by parts".

Nope, still don't get it :(

sbkp
Posts: 29
Joined: Wed Jul 04, 2012 1:29 pm UTC

Re: 1201: "Integration by parts"

Postby sbkp » Fri Apr 19, 2013 4:57 am UTC

Thinking about how much calculus I've forgotten makes me sort of sad. Thankfully the alt text cracked me up and I can forget about being sad for a while.

I totally do not get what the other meaning of "by parts" is.

Kit.
Posts: 1117
Joined: Thu Jun 16, 2011 5:14 pm UTC

Re: 1201: "Integration by parts"

Postby Kit. » Fri Apr 19, 2013 5:02 am UTC

boozledorf wrote:
Kit. wrote:
AluisioASG wrote:Is this supposed to be a joke?
I don't get it (the joke part).

Double meaning of "by parts".

Nope, still don't get it :(

It's only the first half of the actual method (which is useful).

Image

User avatar
keithl
Posts: 659
Joined: Mon Aug 01, 2011 3:46 pm UTC

Re: 1201: "Integration by parts"

Postby keithl » Fri Apr 19, 2013 5:19 am UTC

This is making fun of half-assed thinking about doing integrals. If the functions u and v are chosen so that u is a simple function of v, that makes the integration relatively easy. But the half-ass explainer disappears before teaching how to select the functions, or what they mean. (edit) And integration by parts is a similar-looking method that can sometimes recast an unsolvable integral into a solvable one.

Many of us have had useless teaching assistants like that. Useless math TAs are responsible for creating many business majors, and perhaps a few of the head scratchers reading this forum.

(edit) Me, I just renormalize the problem into a unitless form, approximate it numerically, then throw Mr. Computer at it.

User avatar
Eternal Density
Posts: 5579
Joined: Thu Oct 02, 2008 12:37 am UTC
Contact:

Re: 1201: "Integration by parts"

Postby Eternal Density » Fri Apr 19, 2013 5:40 am UTC

GOOMHR, I was thinking this very thing this morning, as the topic of university math we've forgotten and integration in particular came up at the office.
And now I feel dirty for posting in a thread other than the One about the One True Comic :(

Also, ∫ e^(x) sin(x) dx = -e^(x)cos(x) + e^(x)sin(x) - ∫ e^(x)sin(x) dx
Play the game of Time! castle.chirpingmustard.com Hotdog Vending Supplier But what is this?
In the Marvel vs. DC film-making war, we're all winners.

User avatar
da Doctah
Posts: 983
Joined: Fri Feb 03, 2012 6:27 am UTC

Re: 1201: "Integration by parts"

Postby da Doctah » Fri Apr 19, 2013 6:41 am UTC

Eternal Density wrote:Also, ∫ e^(x) sin(x) dx = -e^(x)cos(x) + e^(x)sin(x) - ∫ e^(x)sin(x) dx


Well, duh!

Wait, doesn't markup here let you do exponents? Quick check:

∫ ex sin(x) dx = -excos(x) + exsin(x) - ∫ exsin(x) dx

tho74
Posts: 13
Joined: Wed Oct 19, 2011 7:20 am UTC

Re: 1201: "Integration by parts"

Postby tho74 » Fri Apr 19, 2013 6:52 am UTC

sbkp wrote:Thinking about how much calculus I've forgotten makes me sort of sad. Thankfully the alt text cracked me up and I can forget about being sad for a while.

I totally do not get what the other meaning of "by parts" is.


The method explained it "integration by parts", but is is only explained partially (by parts, so to say...) I also didn't get it at first :-)

User avatar
The Old Wolf
Posts: 22
Joined: Fri Aug 21, 2009 7:28 am UTC
Location: Not Denver, but we have better powder.

Re: 1201: "Integration by parts"

Postby The Old Wolf » Fri Apr 19, 2013 7:05 am UTC

As a linguist, I flunked out of Calculus in my first year of college, barring me forever from my long-dreamed-of medical career. But linguistics is not all bad. I can conjugate verbs in half a dozen languages faster than I'll ever understand integration, but this formula I will never forget:
Image

A linguist can't ever forget a limerick: clean, dirty, or technical.

Integral zee squared dee zee,
From one to the cube root of three,
Times the cosine
Of three Pi over nine
Equals log of the cube root of e!

I'm told the equation evaluates to 1/3; I'll take the word of my math-enabled friends on that point.
"The greatest insanity is surely to see the world only as it is, and not as it might be."
-Miguel de Cervantes

taemyr
Posts: 111
Joined: Fri Jan 26, 2007 12:14 pm UTC

Re: 1201: "Integration by parts"

Postby taemyr » Fri Apr 19, 2013 7:25 am UTC

The Old Wolf wrote:...
Equals log of the cube root of e!

I'm told the equation evaluates to 1/3; I'll take the word of my math-enabled friends on that point.


That log of the cube root of e equals 1/3 is closer to linguistics than to mathematics. It plops directly from the semantical meaning of the words.

Kit.
Posts: 1117
Joined: Thu Jun 16, 2011 5:14 pm UTC

Re: 1201: "Integration by parts"

Postby Kit. » Fri Apr 19, 2013 7:39 am UTC

Btw...

Vroomfundel
Posts: 117
Joined: Wed Sep 29, 2010 7:36 am UTC

Re: 1201: "Integration by parts"

Postby Vroomfundel » Fri Apr 19, 2013 9:23 am UTC

taemyr wrote:
The Old Wolf wrote:...


That log of the cube root of e equals 1/3 is closer to linguistics than to mathematics. It plops directly from the semantical meaning of the words.


:-D well said, sir, well said

For me personally, I don't know if it was a good or bad fortune that I was never fully exposed to integrals - I studied a math-heavy major that taught calculus in three parts, then moved to CS after part II, when CS had already finished with integrals. Inevitably, I had to deal with some of them as they spring up in every subject that has anything to do with math and physics so got some basic knowledge, which I promptly forgot after graduation.

I also never liked integrals - there was never a recipe, you just juggle with the functions until they start looking like something you can integrate. The only way to get a reasonably good grasp is to just do tons of them until you get intuition.
On the other hand - this brings math closer to art, which, some proponents argue, is what true understanding of a subject means. In the general sense I agree with this - true understanding of maths means being able to percieve the beauty of it. However, I do percieve the beauty of integrals, I admire the elegant ways they represent physical quantities - without actually being good at integrating. For it's always been like those riddles where you have a bunch of letters and you need to find the encoded message. How do you do it? Well, you just brute force all possible mappings between symbols until you detect some pattern that makes sense. What skill does solving these problems demonstrate, beside patience and persistence with mindless tasks? Not that these are not important traits but hardly the ones I'd like to be able to shine with, given the opportunity to choose superpowers.

Like the #CERNJOBSENIGMA:
EIBCC = 5 9 2 3 3 => 59 * 23 * 3 = 4071
WTF? So I'm expected to try out all possible permutations of the numbers at hand and mathematical operations? GTFO

Integrals, of course, make a lot more sense than these mindless riddles - it just felt like this to me in university, when I lacked the intuition to solve them without brute-forcing
lexicum.net - my vocabulary learning platform

Plutarch
Posts: 103
Joined: Fri Apr 17, 2009 10:29 am UTC
Location: London, UK

Re: 1201: "Integration by parts"

Postby Plutarch » Fri Apr 19, 2013 10:55 am UTC

After a long, and quite educational struggle, featuring many xkcd comics where I didn't really get the joke, but managed to get the hang of it in the end, I've finally arrived at one which I will never be able to understand. Other posters' explanations and Wikipedia will not help me this time. :(

MarvinM
Posts: 95
Joined: Tue Jul 29, 2008 11:45 pm UTC

Re: 1201: "Integration by parts"

Postby MarvinM » Fri Apr 19, 2013 12:12 pm UTC

Oh come on, it's really simple guys.

1. Split the product into two parts such that one can be integrated (v') and the other can be differentiated (u).
2. Mumbleandputtheuintheummwhiletheu'vhastobeintegralable.
3. Profit.

User avatar
cellocgw
Posts: 2054
Joined: Sat Jun 21, 2008 7:40 pm UTC

Re: 1201: "Integration by parts"

Postby cellocgw » Fri Apr 19, 2013 12:23 pm UTC

Or just submit the original integral to Mathematica and let it tell you the (analytic) answer.

PS
We in the USA are very accustomed to integration by parts. Only some parts of the USA have ever integrated; others still haven't.
https://app.box.com/witthoftresume
Former OTTer
Vote cellocgw for President 2020. #ScienceintheWhiteHouse http://cellocgw.wordpress.com
"The Planck length is 3.81779e-33 picas." -- keithl
" Earth weighs almost exactly π milliJupiters" -- what-if #146, note 7

Barstro
Posts: 103
Joined: Mon Aug 13, 2012 2:34 pm UTC

Re: 1201: "Integration by parts"

Postby Barstro » Fri Apr 19, 2013 12:27 pm UTC

I wonder if some people have trouble with this comic because it's too simple, or if I'm a fool and only think I understand this.

I like the alt text. My calculus teacher stated that the only time he almost scored a 100 on a math exam, he forgot to put +C at the end and only got a 98. In "honor" of that, he took two points off for every missed "+C" on any exam. By showing all work, it was possible to score less than 0 on some of his tests.

User avatar
Diemo
Posts: 396
Joined: Mon Dec 03, 2007 8:43 pm UTC

Re: 1201: "Integration by parts"

Postby Diemo » Fri Apr 19, 2013 12:31 pm UTC

Thats terrible. I never write in the +C in any intermediate steps in an integral. Just add the dam thing at the end
In the beginning the Universe was created.
This has made a lot of people very angry and been widely regarded as a bad move.
--Douglas Adams

Kit.
Posts: 1117
Joined: Thu Jun 16, 2011 5:14 pm UTC

Re: 1201: "Integration by parts"

Postby Kit. » Fri Apr 19, 2013 12:45 pm UTC

Plutarch wrote:After a long, and quite educational struggle, featuring many xkcd comics where I didn't really get the joke, but managed to get the hang of it in the end, I've finally arrived at one which I will never be able to understand. Other posters' explanations and Wikipedia will not help me this time. :(

It's actually very easy if you know what the derivative is. If you don't, it is still not hard, but may take quite a lot of time to explain. Like... a couple of hours, if you understand what the function is.

That's if you have never created your own map projection. Otherwise it may take forever.
Last edited by Kit. on Fri Apr 19, 2013 1:12 pm UTC, edited 1 time in total.

Ginormous
Posts: 2
Joined: Fri Apr 19, 2013 12:47 pm UTC

Re: 1201: "Integration by parts"

Postby Ginormous » Fri Apr 19, 2013 12:50 pm UTC

If u = v = x, then the final answer is (1/3) * x^3 + c. This is because the original equation reduces to x^2.

I understand that he means the integral remaining after doing the first steps of integration by parts is equal to .5x^2, but that is not the FINAL answer, which is what the comic indicates.

Ginormous
Posts: 2
Joined: Fri Apr 19, 2013 12:47 pm UTC

Re: 1201: "Integration by parts"

Postby Ginormous » Fri Apr 19, 2013 12:52 pm UTC

The Old Wolf wrote:I'm told the equation evaluates to 1/3; I'll take the word of my math-enabled friends on that point.

Here's why. When you take the ln of something that is raised to a power (assuming the power is inside the natural log), you can immediately move the power out of the natural log and make it the scalar. This is because ln(x * y) = ln(x) + ln(y). So, ln(x^3) = ln(x * x * x) = ln(x) + ln(x) + ln(x) = 3ln(x).
In additional ln(e) = 1. So, ln(e^[1/3]) = [1/3]*ln(e) =1/3.

User avatar
Diadem
Posts: 5654
Joined: Wed Jun 11, 2008 11:03 am UTC
Location: The Netherlands

Re: 1201: "Integration by parts"

Postby Diadem » Fri Apr 19, 2013 12:57 pm UTC

Integration by parts is a lot easier if you're a physicist: [imath]\int{dx f'(x) g(x)} = -\int{dx f(x) g'(x)}[/imath]

(I hope I did the latex correctly: It doesn't parse here on my laptop, so I have no idea ;-P)
It's one of those irregular verbs, isn't it? I have an independent mind, you are an eccentric, he is round the twist
- Bernard Woolley in Yes, Prime Minister

AUS
Posts: 36
Joined: Fri Sep 16, 2011 6:38 am UTC

Re: 1201: "Integration by parts"

Postby AUS » Fri Apr 19, 2013 1:05 pm UTC

I don't know much about integration at this point in my life, but I understood the function to the extent that I laughed at the joke. "Yeah..That didn't change..anything.."

Barstro
Posts: 103
Joined: Mon Aug 13, 2012 2:34 pm UTC

Re: 1201: "Integration by parts"

Postby Barstro » Fri Apr 19, 2013 1:17 pm UTC

Diemo wrote:Thats terrible. I never write in the +C in any intermediate steps in an integral. Just add the dam thing at the end


Not that I remember math all that well, but don't you NEED to write +C in there right away? Other functions calculations could alter the +C in the middle of the equation.

Of course, you probably mean to just add +C at the end of each important step, before other functions calculations. Well done, sir. You proved me wrong again.

Edit: see; I cannot even remember the correct words to use in math problems.

User avatar
Xenomortis
Not actually a special flower.
Posts: 1448
Joined: Thu Oct 11, 2012 8:47 am UTC

Re: 1201: "Integration by parts"

Postby Xenomortis » Fri Apr 19, 2013 1:23 pm UTC

If there's an integral sill in there (and you're not dealing with multiple integrals) then you don't really need to.
After all, it's just a constant. It doesn't matter if the +C you have at the end isn't the same +C you had in the intermediate steps. The sum of two (or more) unknown constants is still an unknown constant.
Image

User avatar
Angelastic
Posts: 700
Joined: Thu Nov 03, 2011 8:36 am UTC
Location: .at (let's see what's through here!)
Contact:

Re: 1201: "Integration by parts"

Postby Angelastic » Fri Apr 19, 2013 1:27 pm UTC

This should help you with your +C.
Knight Temporal, and Archdeacon of buttermongery and ham and cheese sandwiches. Nobody sells butter except through me.
Image Smiley by yappobiscuits. Avatar by GLR, buffygirl, BlitzGirl & mscha, with cari.j.elliot's idea.
Haiku Detector
starts a trend to make way for
my robot army.

Herah
Posts: 2
Joined: Sun Nov 04, 2012 3:02 pm UTC

Re: 1201: "Integration by parts"

Postby Herah » Fri Apr 19, 2013 1:33 pm UTC

keithl wrote:This is making fun of half-assed thinking about doing integrals. If the functions u and v are chosen so that u is a simple function of v, that makes the integration relatively easy. But the half-ass explainer disappears before teaching how to select the functions, or what they mean. (edit) And integration by parts is a similar-looking method that can sometimes recast an unsolvable integral into a solvable one.


It's simpler than that. It doesn't say functions u and v -- it says variables u and v. So you're just renaming the original functions without adding any value.

User avatar
Qaanol
The Cheshirest Catamount
Posts: 3069
Joined: Sat May 09, 2009 11:55 pm UTC

Re: 1201: "Integration by parts"

Postby Qaanol » Fri Apr 19, 2013 1:48 pm UTC

Integration by parts is nothing more nor less than the product rule for differentiation, hit with an integral:

(u·v)′ = u·v′ + v·u′
∫(u·v)′ = ∫(u·v′ + v·u′)
uv = ∫(u·v′) + ∫(v·u′)
∫(u·v′) = uv - ∫(v·u′)
wee free kings

pyronius
Posts: 77
Joined: Wed Mar 14, 2012 4:44 am UTC

Re: 1201: "Integration by parts"

Postby pyronius » Fri Apr 19, 2013 1:57 pm UTC

I had a calc TA once who while in the middle of one of the most important chapters of the class looked up at the problem on the board and said something to the effect of "y'all know how to subintegravide the cosquarent parts right?" and then proceeded to rewrite the problem as something that looked entirely different and unrelated. From that point on he did that with almost every problem. When asked about it his answer was "I'm sure one of your classmates can explain it to you"

they couldn't. they absolutely couldn't. needless to say i did not pass that class.

User avatar
drachefly
Posts: 197
Joined: Thu Apr 23, 2009 3:25 pm UTC

Re: 1201: "Integration by parts"

Postby drachefly » Fri Apr 19, 2013 2:06 pm UTC

Diadem wrote:Integration by parts is a lot easier if you're a physicist: [imath]\int{dx f'(x) g(x)} = -\int{dx f(x) g'(x)}[/imath]


Well, assuming the value along the boundary is zero (e.g. you're integrating an interaction cross-section), yes. It still makes me cringe to see that done without making sure it applies each time.

MathUhhhSaurus
Posts: 48
Joined: Wed Dec 08, 2010 8:34 pm UTC

Re: 1201: "Integration by parts"

Postby MathUhhhSaurus » Fri Apr 19, 2013 2:10 pm UTC

ugly (u) vikings (v) vacuum (v) dust up (du)!

∫(u*dv) = u*v - ∫(v*du)

Kit.
Posts: 1117
Joined: Thu Jun 16, 2011 5:14 pm UTC

Re: 1201: "Integration by parts"

Postby Kit. » Fri Apr 19, 2013 2:18 pm UTC

Xenomortis wrote:If there's an integral sill in there (and you're not dealing with multiple integrals) then you don't really need to.
After all, it's just a constant. It doesn't matter if the +C you have at the end isn't the same +C you had in the intermediate steps. The sum of two (or more) unknown constants is still an unknown constant.

It's worse than that, actually. If the function under the integral has a singularity at x0, then C< for x<x0 is not necessarily equal to C> for x>x0, so "+C" is not just a +constant.

User avatar
henre
Posts: 470
Joined: Sun Oct 29, 2006 10:04 pm UTC
Location: A healthy soul clings to a healthy spirit and a healthy body.

Re: 1201: "Integration by parts"

Postby henre » Fri Apr 19, 2013 2:19 pm UTC

I laughed at this comic. I'm actually sitting with calculus homework in front of me right this second.

I <3 Integration by Parts.
An airplane, a puppet, an orange, a spoon,
A window, and outside: stars, and the moon.

ʇɟıɥs sı ʎɹʇ oʇ ʇɟǝl ƃuıɥʇ ʎluo ǝɥʇ sǝɯıʇǝɯos

MarvinM
Posts: 95
Joined: Tue Jul 29, 2008 11:45 pm UTC

Re: 1201: "Integration by parts"

Postby MarvinM » Fri Apr 19, 2013 2:33 pm UTC

Brings back a lot of memories of being taught calculus badly. The teacher felt the need to derive integration by parts, after not teaching calculus from first principles, and that was where the cracks in our understanding showed the most. I was off balance, I'd been taking the addition properties of derivatives and integrals for granted and multiplication did not work the same. Suddenly dy/dx which had been a symbol for 18 months was being broken apart and lone dx bits were being used to justify integration in ways that made no sense at all.

What seemed like half way through the derivation, the teacher stopped and told us what was on the blackboard was the desired result. Then it's then not written how it's used. Why u and v', why not call them u and v and put the integrals on the right hand side so the actual method follows? Then there is remembering the bloody thing, equations are not on the A-Level paper, you have to memorise them. Why are you torturing me like this? What did I ever do to you? It's the combination of so many problems that makes this such nightmare fuel.

User avatar
neremanth
Posts: 157
Joined: Wed Jul 25, 2012 4:24 pm UTC
Location: UK

Re: 1201: "Integration by parts"

Postby neremanth » Fri Apr 19, 2013 3:02 pm UTC

Quicksilver wrote:Alt Text:"If you can manage to choose u and v such that u = v = x, then the answer is just (1/2)x^2, which is easy to remember. Oh, and add a '+C' or you'll get yelled at."
It's been a while since I've done integration, but isn't the formula x^n = x^(n+1)/(n+1) + c?

Yes (I think so, but it's been a while since I've done any too...). But the alt text is still right. If u = v = x then [imath]\frac{dv}{dx}=\frac{d}{dx}x=1[/imath], so [imath]dv=dx[/imath] so the original integral is [imath]\int u dv = \int x dx = frac{1}{2}x^2[/imath] as claimed.

Yupa
Posts: 12
Joined: Fri Feb 13, 2009 4:06 am UTC

Re: 1201: "Integration by parts"

Postby Yupa » Fri Apr 19, 2013 4:02 pm UTC

pyronius wrote:From that point on he did that with almost every problem. When asked about it his answer was "I'm sure one of your classmates can explain it to you"


Having a TA who can't teach is bad. Having a TA who won't try is worse. Did you talk to your professor about the fact that one of his TAs was refusing to do the work he was paid for?

rcox1
Posts: 112
Joined: Wed Nov 11, 2009 11:23 pm UTC

Re: 1201: "Integration by parts"

Postby rcox1 » Fri Apr 19, 2013 4:11 pm UTC

keithl wrote:This is making fun of half-assed thinking about doing integrals. If the functions u and v are chosen so that u is a simple function of v, that makes the integration relatively easy. But the half-ass explainer disappears before teaching how to select the functions, or what they mean. (edit) And integration by parts is a similar-looking method that can sometimes recast an unsolvable integral into a solvable one.

Many of us have had useless teaching assistants like that. Useless math TAs are responsible for creating many business majors, and perhaps a few of the head scratchers reading this forum.

(edit) Me, I just renormalize the problem into a unitless form, approximate it numerically, then throw Mr. Computer at it.


I find the joke to be that in many processes can be taught, but processes do not solve a problem. All they do is provide a means by which a skilled person can solve a problem. I see this a lot with flow charts or "cheat sheets" supplied to students in hope that the process can be dumbed down enough so the student can apply it by rote. Not going to happen. The student has to have some idea of input, purpose and function so the proper process can be applied in the proper way to the given problem. Otherwise everything is AWESOME!!!, and you are just going to pull out a hammer.

Hopefully by the time someone see integration, they have seen enough derivatives to identify the kind of thing that the integration is going to look like. From there a method can be selected to get you to the full solution.

It is interesting that Integration by Parts is no longer tests on the AP Calculus exam. It is really about internalizing enough information to "know" how to break up the problem. And this why I like this. Anytime we can be retaught that the best way to solve a problem is to break it up into pieces, good things are going to result.


Return to “Individual XKCD Comic Threads”

Who is online

Users browsing this forum: Cougar Allen, Majestic-12 [Bot], moody7277 and 43 guests