What is your favorite integration technique? I like to integrate by parts.
hows highschool, anon?
>>8075922
I don't like to integrate.
>>8075922
i don't like it at all. it was nice when shit was easy but when the trigonometric madness begins, the fun is over.
>>8075943
At what point in Calculus do I really need a mastery of trig identities and pricing trig stuff? I'm taking calc I next semester and seriously need work on this.
>>8075948
Proving, not pricing.
>>8075948
for me it is calc 2, but i don't know whether it's the same everywhere. put on your jacket as soon as you hear about riemann sums and improper integrals.
>>8075922
I usually can see the integration if the function is fairly obvious, but parts is my preferred. For whatever reason I hate substitution. Pretty cool equations have been discovered with parts.
My favorite is integration by parts too.
LIATE
>>8075922
By the FTC.
>>8075948
All you really need is the Pythagorean identity, Euler's identity, De Moivre's formula, and rudimentary algebra knowledge to derive any trig identity you want. The current pedagogy complicates the trig stuff in integral calculus imho
>>8075948
I never had to prove a thing in any of my calc classes (I, II, vector) or differential equations. So, not at all I guess. I also never really needed to know trig identities until calc 2, and then, all I really needed to remember was sin^2 + cos^2 = 1. You can derive most of the commonly needed ones from that.
>>8075948
You need to have a good standing with trig in calc 2.
You will be doing stuff like inverse trig derivatives and integrals (mostly new identities) and trig substitution.
You should ask your professor after day one if you arent sure about your trig skills.
>>8075922
numerical integration
>>8075922
Honestly? I would have to say triple integration in spherical coordinates. They have a special place in my heart.
Let me tell you a story Anon:
I am naturally terrible at math, so of course I gravitated towards it because being bad at sometime upsets me on a fundamental level.
I started at the very bottom of the college math scale: MATH103 college algebra. Any lower would have been remedial math, no credit. I was almost definitely the only kid in there who spoke mother-tongue English. Now I'm finishing my fourth-year math degree requirements, I went from the very bottom to the very top (of undergrad at least)
Anyways, when I used to enter the classroom for Precalc, the previous class had been Multivariable Calculus. I was utterly, hopelessly fascinated by the alien symbols left on the board, and the fact that the professor drew amazingly intricate curves and spheres and more complex 3D shapes using several colors of chalk. They were brilliant detailed and beautiful; the professor had clearly missed a higher calling in art. I later found out that particular professor had a reputation for going all-out with the lecture drawings, to the extent that the lecturing actually suffered, but regardless it was a sight to behold. I found myself trying to get to class as soon as possible so I could get a glimpse of the board before he erased it. I longed for the day when that board would make sense to me.
Imagine pic related but with more shading and multiple lines with different colors.
Three years later when I got to triple integrals in spherical coordinates, it was like "You made it Anon. After thousands of problems and hundreds of hours of almost-religious study you finally understand what was on that board." It was a pretty amazing feeling
>>8075922
I like integrating using my scientific calculator
>>8076019
>be me
>say pic related
>forget pic
>>8076019
Are you kidding? Double and triple integration in special coordinates is first term undergrad.
>>8076028
We do it in Calc III: Multivariable here, which is probably first semester second year.
Calc I: limits, differentiation, applications of differentiation, and integration
Calc II: Basically integral calculus with sequence and series, lots of application problems
Calc III: vector calculus, multiple integrals, theorems of Stoke and Gauss and Green
It doesn't matter though, the point is I like triple integrals in spherical coordinates and you can't take that away from me
>>8076037
Ah I see.
Here it's a bit different, your calc I and II and "multiple integrals" is first term first year, then first term second year is your calc III with "multiple integrals" being replaced by complex analysis.
I'm just surprised that someone who's almost finished university still likes triple integrals in any coordinates. I found it a useful tool in special cases, but otherwise it didn't hold any particular meaning for me.
Mathematica
>>8076019
Same here, anon. I had to drop out of calc in 12th grade after holding on with a c-/d then getting obliterated by the chain rule. I also started with College Algebra, and had the highest grade in the class, I kind of wish I would have started with PreCalc. I was planning on taking a semester of just trigonometry but decided to skip it. really liked the teacher and enjoyed the class though. Fall will be my second attempt at Calculus 1.
>>8076019
good on you, mate. I wish you luck in your further study.
>>8076086
good luck anon, it can be done. I entered college with mediocre math grades and started at pre-calc. I was always terrible at math all throughout school but with enough enough blood and sweat I've grown to love and will be graduating with a math degree next year with around a 3.8 gpa. If I can get an A in calc 1, so can you
>>8076028
yeah lol. i never understood why people talk about double integrals as if it was something higher. it's literally the same as normal integrals with the only difference being that you do it twice in a row.
This is like asking a mechanic what his favorite way to unscrew a bolt is.
It's a necessary skill for anyone working quantitatively, but it's boring and tedious and a tool rather than an object of study.
>>8076222
>implying the op was about lebesgue integrals
>>8076241
>implying the op specified a particular integral
>>8075948
I think people grossly exaggerate calc 2's trig difficulty, theres like 4 memorizable formulas for reducing powers of sine, cosine etc, and then all you gotta do for trig subs is DRAW A FUCKING TRIANGLE
if you know sin^2 + cos^2 = 1 you're good
>>8076205
>it's literally the same as normal integrals with the only difference being that you do it twice in a row.
Assuming the function satisfies Fubini's theorem, of course.
>>8075922
By substitution. Elegant.
>>8076247
Don't be an aspie
>>8076299
autism
>>8075947
but with that pic you actually prove you're from pol. retard.
>>8076304
How is it autistic? It's needed for the proofs of the fundamental theorems in vector analysis.
>>8075922
f(x)
>>8076318
because you don't need it. if it involves anything where half a page is just definitions and stuff like "n-manifolds" come into play, it's autism. limits are the final frontier of healthy maths, everything beyond that is autistic rambling.
>>8076333
So anything beyond your first mathematics course is autistic?
Nice one.
>>8076337
Did you just tried to overflow my refresh rate?
>>8076340
No. I was trying to insert sourcecode. But I guess /sci/'s latex does not support it.
>>8076333
>hurr durr it's too difficult for me to understand it must be autistic
jesus fucking christ, definitions are there to make things concise and easier for us, are you an engineer or something?
>don't tell me the proof just tell me the theorem
Integration is fucking boring.
Honest, what is the point of learning these technqieus? Any actual function used to model a real world phenomena would likley never be as pristine and perfect as are all the functions that allow for integration.
>>8075922
Writing it in wolframalpha
Why is there an integration thread without Cleo?
http://math.stackexchange.com/users/97378/cleo
>>8076415
That's like saying, what's the point of learning multiplication table if most real world applications will not be using integers.
>>8075922
>What is your favorite integration technique?
https://en.wikipedia.org/wiki/Simpson%27s_rule
>>8076428
This is a highschool technique, I don't think you need to link it unless you want to get an underaged ban.
>https://www.4chan.org/rules#global2
>>8076435
Yeah, I learned it in high school, but I never used it until I got a job after college. It's pretty accurate for a such a simple method.
>>8075936
Are you a mudslime immigrant?
Trig sub, nigga.
Cause it's cool, and you actually use it sometimes.
>>8076420
Interesting stuff, but are her answers even useful without her methods?
>>8076397
>don't tell me the proof just tell me the theorem
there is literally nothing wrong with that. if it works, it works and nothing else is needed.
>favorite integration technique
Applying branch cuts and evaluating the residues.
>>8076268
And then there's 6 more series tests (this is what I was awful at)
And all those named series that are so similar
>>8076771
Are you sure you're a mathematician?
IBP. Use it all the time in Quantum Probabilities and I just us the handy formula but still bust out the uv-int(vdu) sometimes
>>8076268
I remember my professor made us memorize the reduction formula for secant and tangent which was hell
>>8076881
What's that?
>>8076891
I think he said his professor doesn't teach how to derive sec and tan
>>8075997
>we wuz stewarts
>>8076268
Most people are idiots. Before I actually entered university, I heard about people finding calculus I and II difficult... IRL and here. I realize now they were just normal people doing shit degrees, idiots who made the mistake of choosing math, or engineers.
>>8075943
Dude trig substitutions was the coolest
Half-Angle Substitition tb.h
Uhh, no one's said Stoke's yet? Not out of Calc II are we?
[math] \int_A \nabla \times \vec{F} \cdot d \vec{a} = \oint_L \vec{F} \cdot d \vec{l} [/math]
cauchy theorem
>"durr this integral is hard so lets just draw a circle around it in the complex plane"
>it works every time
goddamn witchcraft
>>8077867
>Stoke's
>only vector analysis
>>8077880
>he can't prove Cauchy's Theorem so it looks like witchcraft to him
>>8076015
This.
>>8077902
i went through the proofs when i took complex and it all checked out but cmon, that shit is basically cheating and you know it
>>8077907
Really? How did you proof go?
We had used results from vector analysis (Green's Theorem and Divergence Theorem) along with the fact that holomorphic functions are harmonic and a vector representation of complex numbers.
It was magic in that all of the results fit in together so nicely to give Cauchy's Theorem.
>>8077907
what proof?
you just have to prove the other integrals equal zero for r->inf or you have to know their value thats it
>>8075941
There was a tenth grader in my graduate topology course.
My friend was taking real analysis in 12th grade and his 3rd grade brother was taking pre-calculus.
You should know how to integrate.
>>8075922
Lebesque integration.
Are you all retarded?
>>8076297
He's not. Lebesque integrals are more useful and the obvious reference when someone says "integral."
>>8076279
Just learnt this for an exam coming up, figured its about time I understood what is going on.
The lecturer was really awful with teaching and nobody understood what was going on or the topics he was teaching.
Got myself a book, did some searching and found out he's teaching the equivalent of calcIII so I pulled all the topics for it and started from scratch. So far its quite nice, I always liked calculus in general.
>>8076966
>finding calc I/II hard
Second year EEE here, everyone suffers in maths but generally I blame the poor teaching and/or marking. Granted most engineers drop big marks for maths, but literally a book could replace all eng maths and we'd do better.
I handed in some work and didn't make a single mistake, not a single cross to be seen, but incredibly only got 80% because the lecturer said I "assumed somebody who knew about maths was marking it". I derived from as far back as I could go but I wasn't about to prove multiple trig identities from scratch because I had to use so many (which I referred to each time) in some questions, particularly if the person marking it wouldn't have known maths, whatever the fuck that's supposed to mean.
tl;dr engineers get fucked over with maths because some can make up for lazy maths with other classes (bad idea) and the teaching is hardly ever good or contextual in the first place. There's a lot of 'coasting through'.
>>8078169
>Granted most engineers drop big marks for maths
really? here (imperial college) maths is definitely one of the easiest classes.
>>8078176
It is often ez, but somehow people still drop marks all over the place for it. Not sure if its because our maths papers are marked by the maths dept who look for derivations and proof more than problem solving which is what we're mostly asked to do.
Bearing in mind that there are still people in second year who have difficulty associating standard form with micro/nano/pico prefixes.
>tfw ask someone to get the closest capacitor available to the 1×10^-10 I calculated we needed
>what is that then?
>NANO ITS 10 FUCKING NANO
Incredible considering we use them daily.
>>8078190
*0.1nano fml spending so much time like this
>>8078141
>What is your favorite integration method?
>You should know how to integrate
What?
Reduction formula ftw
>>8078136
That's Cauchy's Integral Formula, not the same thing.
>>8077867
Stokes and Greens Thms are based
t. Antenna Engineer
>>8076568
underrated
>>8076771
>engineer detected
>>8077900
That image sums up every explanation of string theory I've ever heard
Tabular method is the shit when it works
Partial fractions, for sure. They take a bit of time but are fun and look good on paper.
>>8076568
>>8078141
You all sound like sperg "savants"
>>8078141
>Child prodigies are the norm
K sperglord
residue theorem
>>8077867
Sorry, don't you mean the real Stokes theorem?
[eqn]\int_{\partial \Omega} \omega = \int_{\Omega} \mathrm{d}\omega [/eqn]
>>8079643
I was hinting at it. Foreplay if you will. That right there, the real Stoke's theorem, is pretty much all of calculus in a single line.
>>8079646
yeah it's pretty fuckin rad
Hello I am just starting to learn integration in my business calc class and it is confusing. What is the easiest most retard proof method of solving these?
>>8076784
I wasn't great at series either so I just did a million until I got good at recognizing whats what, but there werent any problems in the book like the ones my professor'd assign with power towers and shit
>>8075922
Feynman parameterization, Schwinger proper-time integral and generally anything that expresses the integrand as an integral.
>mfw making mathematicians squirm by exchanging orders of integration without confirming the integral's convergence
>>8076420
Is the Cleo character associated with the Wolfram Alpha?
Is the Cleo character not a human, but instead an application of the Wolfram Alpha?
>>8080124
It's not much harder than differentiation once you get it.
Learn how to transform variables, integration by parts, partial fractions, and you should be all set. And trig integrations I guess. That's it.
>>8075922
i dont even remember how to do it
>>8079603
>Thinking that most integrals are analytically solvable.
in many cases, (outside of homework problems) things aren't always so neat. try to integrate x^x^2 without numerical methods.
I like the Runge-Kutta-Fehlberg Method because it has some neat applied math and is pretty accurate. Also there's something satisfying about first degree newton cotes with 10,000 steps
>>8080450
Some say Cleo works in a Russian military bunker so doesn't have time to type up their method.
>>8075922
Line integrals
T A B L E M E T H O D
>>8075941
Nice shitpost fgt kys rn
>>8075922
Really, OP?
There are few cases (like logs) where integration by parts is actually convenient, and so many cases where it gets you nowhere.
I'd say my favourite is trigonometric substitution or partial fractions. Euler's method is nice too.
>>8075922
differentiation under the integration sign because i'm not a sheep like the rest of you
>>8081986
Euler's method is a myth spread by butthurt engineers
>>8075922
Who the fuck likes integration by parts? My favorite is substitution where it fits like a glove.
>>8075922
This is for my niggas majoring in applied math:
https://youtu.be/2I-_SV8cwsw?t=47
implicit integration is best integration
I like to integrate whilst getting my cock sucked
>>8075922
runge kutta
>>8076015
this kills the mathematician
>>8076420
fillin'' it up
>>8076420
Cleo is just Tung Fey. If you approach him about it he will get defensive. I have also happen to have evidence but I don't care anymore.
>>8081267
found the oldfag
>>8078108
not that anon, but in my class we used Goursat's integral lemma for triangles which is Cauchy's theorem for triangles essentially, and the proof was fuckin cool, using infinite converging triangles
