What is your favorite integration technique? I like to integrate by parts

My favorite is integration by parts too.

LIATE

By the FTC.

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

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.

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.

numerical integration

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 user:
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 user. 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

I like integrating using my scientific calculator

>be me
>say pic related
>forget pic

Are you kidding? Double and triple integration in special coordinates is first term undergrad.

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

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

Same here, user. 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.

good on you, mate. I wish you luck in your further study.

good luck user, 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

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.

The hard part is literally just understanding how to parametrise the region.

>regulated integrals
>lebesgue integrals

>implying the op was about lebesgue integrals

>implying the op specified a particular integral

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

>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.

By substitution. Elegant.

Don't be an aspie

autism

but with that pic you actually prove you're from pol. retard.

How is it autistic? It's needed for the proofs of the fundamental theorems in vector analysis.

f(x)

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.

So anything beyond your first mathematics course is autistic?
Nice one.

Did you just tried to overflow my refresh rate?

No. I was trying to insert sourcecode. But I guess Veeky Forums's latex does not support it.

>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.

Writing it in wolframalpha

Why is there an integration thread without Cleo?
math.stackexchange.com/users/97378/cleo

That's like saying, what's the point of learning multiplication table if most real world applications will not be using integers.

>What is your favorite integration technique?

en.wikipedia.org/wiki/Simpson's_rule

This is a highschool technique, I don't think you need to link it unless you want to get an underaged ban.
>Veeky Forums.org/rules#global2

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.

partial fraction decomposition because it reduces calculus to a linear algebra problem.

he proves that at best he is a jewish themed troll. pls read subext.

Are you a mudslime immigrant?

Trig sub, nigga.

Cause it's cool, and you actually use it sometimes.

Interesting stuff, but are her answers even useful without her methods?

>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.

And then there's 6 more series tests (this is what I was awful at)
And all those named series that are so similar

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

I remember my professor made us memorize the reduction formula for secant and tangent which was hell

What's that?

I think he said his professor doesn't teach how to derive sec and tan

>we wuz stewarts

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.

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

>Stoke's
>only vector analysis

>he can't prove Cauchy's Theorem so it looks like witchcraft to him

This.

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

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.

what proof?
you just have to prove the other integrals equal zero for r->inf or you have to know their value thats it

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.

Lebesque integration.

Are you all retarded?

He's not. Lebesque integrals are more useful and the obvious reference when someone says "integral."

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.

>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'.

>Granted most engineers drop big marks for maths
really? here (imperial college) maths is definitely one of the easiest classes.

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.

*0.1nano fml spending so much time like this

sounds like an easy mistake to make :P

but our dept. is self contained so everything is marked internally (and all the papers are anonymised) so it's a lot better than what I hear about US unis.

>What is your favorite integration method?

>You should know how to integrate

What?

Reduction formula ftw

That's Cauchy's Integral Formula, not the same thing.

Stokes and Greens Thms are based

t. Antenna Engineer

underrated

>engineer detected

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.

...

You all sound like sperg "savants"

>Child prodigies are the norm

K sperglord

residue theorem

found the engineers

Sorry, don't you mean the real Stokes theorem?
[eqn]\int_{\partial \Omega} \omega = \int_{\Omega} \mathrm{d}\omega [/eqn]

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.