help-13

[dire geode]

Pretty sure this is what Camil meant

We learning cryptography now

[hollow osprey]

why the lol

[wraith crypt]

i'm looking up math 55

and it looks really interesting

[hollow osprey]

hav u taken abstract alg

[wraith crypt]

i had something like that in my year 1

[wraith crypt]

yes

[hollow osprey]

is it fun

[wraith crypt]

depends on whether you like algebra?

[hollow osprey]

do you?

[flint plinth]

Just looking at the titles of the lectures for the abstract algebra half, that's pretty hardcore for undergraduates, let alone freshmen... https://canvas.harvard.edu/courses/75936/assignments/syllabus They even get to do some character theory!

[hollow osprey]

lecture 1 is groups

[wraith crypt]

personally i don't have much of an intuition for algebra, so i only did groups through modules and fields, and some lie algebra, and stopped

[flint plinth]

Good grief, I didn't even know this fact about non-abelian finite groups, that at most 5/8ths of the possible pairs of elements commute, and that inequality is sharp.

That's on homework 2

[wraith crypt]

ironically i found rings horrible, but lie algebras quite exciting, though maybe part of that is because the lecturer was much faster

[gentle lintel]

i’m doing chad’s final exam

can i simply leave the key insights down

i don’t want to work out concrete values 😦

[hollow osprey]

yeah

no one stopping you lol

[wraith crypt]

that actually looks really fun

[flint plinth]

Yeah, now it looks fun, after I've already taken two courses in group theory. As a freshman I would have run screaming.

[hollow osprey]

what's the prereqs for this class?

[wraith crypt]

as a freshman i would have totally welcomed it

but my experience is atypical

[flint plinth]

I think no formal prereqs, just "Mathematics 55a is an intensive course for students who are comfortable with abstract mathematics."

[hollow osprey]

guys what would be the normal progression for a first year math major

like calc 3 / diff eq / lin alg -> then what

[flint plinth]

I think I would have enjoyed something at about half this pace, actually, this just seems way too intense, especially if you're taking 4-5 other classes at the same time

[wraith crypt]

my course load in my very first sem, was five courses each covering the equivalent contents of four semesters

that pattern carried on to the second sem

[flint plinth]

Yikes, did you ever sleep?

[wraith crypt]

on average maybe four hours?

it was a hard year

[hollow osprey]

4 hours of sleep for a whole year?

[wraith crypt]

no, for two semesters

winter and summer break, what do you think i spent time doing?

[hollow osprey]

9 months?

catching up? idrk

[wraith crypt]

sleeping and in winter break, prep work

[flint plinth]

Winter and spring break would have called for hibernation with a schedule like that 😁 And I guess some video games

[gentle lintel]

for the first one, notice $\sin^2x = \frac{1 - \cos 2x}{2}$. everything is simple afterwards

[wraith dagger]

Chromium

[hollow osprey]

yep

[wraith crypt]

you ain't wrong, i watched a crap ton of anime to destress

[gentle lintel]

fot the second, $\frac{1}{x^3 + x^2 + x} = \frac{1}{x} - \frac{x + 1}{x^2 + x + 1}$.

[wraith dagger]

Chromium

[hollow osprey]

second one you might actually wanna just finsh

[gentle lintel]

everythnig should also be simple

[hollow osprey]

cuz its not very hard

[gentle lintel]

linear/quadratic -> break it into two integrals, one with u sub one with trig sub

[hollow osprey]

but yeah in essence that's it

but PFD would be easier than the integrals themselvesl ol

[gentle lintel]

x^2 + x + 1 i doubt you can do PFD

[gentle lintel]

this is just an observation

[hollow osprey]

ik. you already did PFD (the easy part) and you skipped the hard part (the integrals)

[gentle lintel]

how are the integrals hard

[hollow osprey]

they rnt but would be more challenging then just algebraic PFD

anyways what did you get for next Q

[gentle lintel]

2?

[ripe stone]

can anyone help me?

[gentle lintel]

2a just average the tip and tail of the line segment.

[hollow osprey]

#❓how-to-get-help

[ripe stone]

this has four lines of symmetry right

[gentle lintel]

this channel is occupied.....

[ripe stone]

oh ok

[gentle lintel]

the integrals should correpond to this

[ripe stone]

how do i get help

[gentle lintel]

❓how-to-get-help

[wraith crypt]

#❓how-to-get-help

[gentle lintel]

❓how-to-get-help❓how-to-get-help

[hollow osprey]

❓how-to-get-help

[gentle lintel]

anyway

2b, just sum some rectangles, some triangles, and a semicircle

2c: F'(5) = 4

2d: it's the perimeter of the semicircle

[fallen heath]

it'd be better to work out the specific values if intending to assess yourself

[fallen heath]

For example this one :o it's not really finished with that

chad, what's the time allotted for the exam?

2hrs?

3?

[hollow osprey]

not sure

but it would prob be 2 hours

[wraith crypt]

paper like this, no more than 2 hours, but 90 minutes feels more likely

[fallen heath]

camieee 2hrs is okay lol

[wraith crypt]

...where i'm at, 60 to 75 minutes for this kind of paper is expected y'know

i'm being kind with 90 HAHA

[hollow osprey]

yeah i think the TA's period would be around 90 mins

but that would be if he was taught all this stuff in a class and prepared for this final (which he wasn't)

so i think 2 hours is fine

[wraith crypt]

2 hours is fine if chromie was actually writing down the full solutions and not...y'know

also, i'm looking at 55a and 55b and now i wish i took it hnnng

[fallen heath]

I believe chromie should realllyyyy write the answers at least

[cedar kiln]

@gentle lintel Has your question been resolved?

[fallen heath]

2 d) I believe is also a fun one :o

[gentle lintel]

.

[fallen heath]

._. what's the answer for 1 b)

[hollow osprey]

he just did the PFD and then said "integral is trivial"

for 1b

[fallen heath]

lmao

[hollow osprey]

not even joking you can scroll up lol

[fallen heath]

more like, if you really wanna assess but also haste through it, just give us the answers and spare the solution lol

[hollow osprey]

true but he just wanted to make sure he got all the big picture concepts

[gentle lintel]

i believe integral of (linear)/(quadratic) is easily generalisable

[hollow osprey]

do it.

[gentle lintel]

so yea, won’t dwell on that lol

[hollow osprey]

$\int \frac{ax+b}{cx^2+dx+e}$

[wraith dagger]

Shuri 4 honorable (Yottachad)

[hollow osprey]

generalize this

[fallen heath]

lmfao

[hollow osprey]

it would take a while but it might be fun?

[gentle lintel]

basically, split it into two integrals
one doable with u sub (int (cx + dx + e))/(cx + d + e)

[hollow osprey]

lot of constants you would have to work with however

[gentle lintel]

the other with trig sub

[hollow osprey]

trig sub? you mean formula

[gentle lintel]

(it won’t, it’ll be boring)

[gentle lintel]

yea, kinda

i don’t memorise those

[hollow osprey]

$\int \frac{1}{u^2 + a^2} = \frac{1}{a}\tan^{-1}\qty(\frac{u}{a})$

this one is good to know IMO

[wraith dagger]

Shuri 4 honorable (Yottachad)

[hollow osprey]

this is the only one i have memorized

and the integral of ln(x) cuz that one shows up a lot (and its not super standard)

[gentle lintel]

yea

for 3, solid of revolution in terms of y coordinates
goes from -√3 to √3, 4 - y² - 1² is the integrand i believe

for 4, only (b) is true, i think

(based on the given information)

5 involves work stuff, i’m not familiar

6b, i don’t know what a centroid is

for 6a, (√(1 - (y - 2)²/4), y) are on the given part of the ellipse

one can easily craft a solid of revolution formula

[wraith crypt]

center of mass

[gentle lintel]

(nor do i know that ;-;)

[dire geode]

not doing very well on this final so far 😐

[wraith crypt]

LOL

[gentle lintel]

for 7, √(1+(f’)²) gives a perfect square

,rotate

[gentle lintel]

(rough work, if anyone’s interested)

[gentle lintel]

(have i provided incorrect answers/approaches)

[fallen heath]

time's not over yet and we don't have all your answers either

cheating not allowed lol

[gentle lintel]

i didn’t cheat

[dire geode]

i'll 🤐 until you're done

[gentle lintel]

(8, 9 involve diff eq, i haven’t touched those either ;-;-;-;)

here’s 10a

,rotate

[gentle lintel]

2+C turns jnto C

[gentle lintel]

10a(ii)can be done using IBP, and this result

[fallen heath]

we really don't have any answers so I'm not sure how anyone's supposed to grade lol

chromium, are you really that averse to solving the paper?

[wraith crypt]

i, too, would like to read full solutions when grading

believe me, there's a reason why i rather enjoy giving zeroes to incomplete scripts

[fallen heath]

coz if so, I'd like to do proceed things your way, adding a "how?" to all your methods so far :o

[dire geode]

Camil's getting paid in handing out zeros to chromi

[fallen heath]

lmao

[wraith crypt]

XD

[hollow osprey]

btw 7 can also be done by hyperbolic cosh / sinh

few things to notice

sinh^2-cosh^2 = 1

d/dx sinh(x) = cosh(x) and d/dx cosh(x) = sinh(x)

and that cosh(x) is just e^x's even part, and sinh being e^x's odd part

that is.

cosh(x) = (e^x+e^-x)/2 and sinh(x) = (e^x-e^-x)/2

[fallen heath]

examiner provides hints moment

[hollow osprey]

ikr 😮

[wraith crypt]

oh, are we grading already?

[gentle lintel]

yea i noticed that

10b is done by induction, but i’m stuck in some int (int f dx) dx situation

it’s a 4 point problem, even lower than q1

i believe i’m overlooking something obvious

[wraith crypt]

well, that's an exam for you

[gentle lintel]

or is it not induction at all

wtf

[fallen heath]

welp, 20 minutes left and we still don't have any answers from you

[gentle lintel]

i’m struggling to do 10b

lmao

@dire geode just point out my mistakes

i’ll attempt another paper later

[fallen heath]

we literally can't lmao, no one's got any clue what you did

[fallen heath]

Can I? can I? can I?

🥺 👉 👈 pweaseee

[dire geode]

.

[wraith crypt]

you go ahead, i got an integration bee in a week to judge and have my own fun

[dire geode]

MIT integration bee?

[fallen heath]

integration bee

[wraith crypt]

nah, knockoff of MIT's

[dire geode]

https://www.quora.com/What-is-it-like-to-participate-in-MITs-Integration-Bee

does sound fun

[fallen heath]

$\int \frac{e^x}{\ln x} \dd{x}$

[fallen heath]

Amen.

[dire geode]

But I soon learned that it's much harder to do calculus in the front of the room when the pressure is on.

[gentle lintel]

ibp

i think

[hollow osprey]

10b is just IBP

no induction needed (it also wouldn't be expected)

[fallen heath]

[hollow osprey]

Lol

[hollow osprey]

this feels non elementary

,w integral of e^x/ln(x)

[wraith dagger]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Yottachad#6969

[hollow osprey]

i was right!

a u sub gets you that nice

$\int \frac{e^{e^u} \cdot e^u}{u} \dd u$

[wraith dagger]

Shuri 4 honorable (Yottachad)

[hollow osprey]

and this is pretty non elementary

looking

[fallen heath]

Indeed it was: the integrand was simply the derivative of x² secx.

those moments when your familiarity with integrals and the practice pays off

.
.
.
kept telling myself, don't fuck up at the beginning, because there's so little margin of error on the easier integrals.

damn, int bee looks scawy

ntm, JEE calculus papers are scawy enough

[wraith crypt]

i don't like that type of competition tbh

i like the type where i can sit down for five hours and do five questions

[hollow osprey]

!?

Sounds like university homework

[fallen heath]

me imagining chromi interrogating about the proof for distributive property of determinants

[gentle lintel]

oh yea

can i try some uni hw

[fallen heath]

Did you finish the paper?

[gentle lintel]

calc1-2 stuff

[hollow osprey]

this is the bonus question

[gentle lintel]

which is

[gentle lintel]

everything i think i’m able to do, yea

[hollow osprey]

Prove that $\frac{x}{1+x^2} < \tan^{-1}(x) < x \text{ } \forall x \in \mathbb{R}^+$

[fallen heath]

FAILED TO RENDER

[gentle lintel]

lmao

[fallen heath]

no bonus question ;-;

oof

[wraith dagger]

Shuri 4 honorable (Yottachad)

[wraith crypt]

https://www.imc-math.org.uk/

[hollow osprey]

where do i see problems

[dire geode]

how about 1 question for 5 hours

[hollow osprey]

my guess. i think its pi^2/6

[wraith crypt]

scroll down to access previous year problems

[dire geode]

answer

[hollow osprey]

https://www.youtube.com/watch?v=k-nrEd3zgOc

[fallen heath]

or 1 question throughout your life: $$\text{Prove collatz conjecture.}$$

[hollow osprey]

least i got the pi^2 right

[fallen heath]

everyone QED lmao

[hollow osprey]

Prove that $$\text{all nontrivial zeros of the } \zeta(s) \text { function have a real part of } \frac 12.$$

[wraith dagger]

Shuri 4 honorable (Yottachad)

[hollow osprey]

+300 iq + $1,000,000

[fallen heath]

lmao

[gentle lintel]

how do we incorporate calculus

[fallen heath]

How did you do this one?

[hollow osprey]

integrals/derivatives

and being REALLY smart with the inequalities

[fallen heath]

$\int_0^{2\pi} \sin^2 \theta \dd{\theta}$

[hollow osprey]

i think he said trig identity

(power reduction)

[foggy merlin]

or sinx = (e^ix - e^-ix)/2

[fallen heath]

lmao

[hollow osprey]

then does it become a complex integral

[gentle lintel]

double angle

[foggy merlin]

nah

[gentle lintel]

consider cos 2x

[hollow osprey]

no contour integral!/

[gentle lintel]

ndkdjdknfnnfckc

what the fuck

[fallen heath]

$=\int_0^{\pi} (1 - \cos 2\theta) \dd{\theta}$?

[foggy merlin]

/2

[wraith crypt]

i find myself amused

[gentle lintel]

alright

[dire geode]

Camil tomorrow: automatic 0/100 for chromi. no cheating allowed

[gentle lintel]

something like that

[fallen heath]

wdym something like that?

[gentle lintel]

sin² = (1 - cos2x)/2, basically

just use this

[hollow osprey]

WHAT?????

[gentle lintel]

integral is then solved easilt

[fallen heath]

sin²x = (1 - cos² x)/2?

[hollow osprey]

HE IS INVENTING TRIG!

okay

[fallen heath]

ahem

[hollow osprey]

now its correct

[fallen heath]

okay umm

I still don't understand what's wrong with $$=\int_0^{\pi} (1 - \cos 2\theta) \dd{\theta}$$

[gentle lintel]

i haven’t checked the bound changes and all

[hollow osprey]

he already accounted for the bounds i think

[gentle lintel]

but this is the main insight to solving

[hollow osprey]

is the area from 0 to pi = to the area from pi to 2pi?

[gentle lintel]

yes

[hollow osprey]

then he already halfed it

so ur answer is still fine ansh

[fallen heath]

aight

next ??

what did we do with this I wonder :o

[sick ruin]

Holy pain

[hollow osprey]

i told someone

[gentle lintel]

1/x - (x + 1)/(x² + x + 1) is the main insight

[fallen heath]

wrong

[hollow osprey]

chromium pfd'd it and then called the rest trivial

[fallen heath]

0 for this one ig :/

[hollow osprey]

RIP that's like

[gentle lintel]

is this wrong lol

[hollow osprey]

10% of the test right there

[fallen heath]

Yeah

[gentle lintel]

i don’t think it is

[sick ruin]

How is that wrong

[fallen heath]

It is

[gentle lintel]

or am i failing algebra

[fallen heath]

You're failing English lmao

[dire geode]

chromi tomorrow: axiom of choice, the rest is trivial

[fallen heath]

It is not the main insight

[gentle lintel]

乾脆不用英文算了

[sick ruin]

😟

[gentle lintel]

there, for those with ocd

[fallen heath]

so umm

[wraith crypt]

...is chromie suddenly chinese?

[foggy merlin]

[fallen heath]

nope, it's still not the main insight

[gentle lintel]

it is to me

[fallen heath]

no matter what you do :/

[hollow osprey]

this is gonna be chromum the day after that

[fallen heath]

Nope

[sick ruin]

I love this

[gentle lintel]

that’s split into two integrals, correct?

the former is ln x

[foggy merlin]

genius

[dire geode]

if he were, he'd be doing better on this exam

[fallen heath]

could you explain how you plan to do $$\int \frac{x+1}{x^2 + x + 1}$$ ?

[gentle lintel]

yea

[wraith crypt]

HAHAHA

[fallen heath]

Lmao

[gentle lintel]

https://m.youtube.com/watch?v=VUaujlcAosQ

[hollow osprey]

LOL

[gentle lintel]

generalisation here

[fallen heath]

:o

sure ig

[hollow osprey]

but do you know how to do that?

[gentle lintel]

i’m too lazy to explain

[foggy merlin]

Vertex form on the denominator

[fallen heath]

oh right :o

[wraith crypt]

until and unless i have some proof you know how to do it, i will still give a 0

it's grading

no hard feelings

[foggy merlin]

and you do some shits to obtain arctan and log

[fallen heath]

0 for this one, yeah

[gentle lintel]

(at this point i could just copy from the sent video and you wouldn’t know, so 0 me i guess)

but i just looked it up

[hollow osprey]

-100% cheating

[gentle lintel]

so uh believe me or not

lol

[fallen heath]

what about this?

how?

[gentle lintel]

(2-4)/2

=-1

[fallen heath]

why?

[dire geode]

so how do you feel about your assessment so far

[gentle lintel]

not bad

i fail enlgihs

uhh

[fallen heath]

umm?

[gentle lintel]

average of linear of [a, b]

is 1/2 (f(a) + f(b))

[fallen heath]

what's the average of "f" defined as anyways

[hollow osprey]

1/2???

[gentle lintel]

i could do an integration

[gentle lintel]

yea

[gentle lintel]

1/(b - a) int f [a, b]

[hollow osprey]

oh wait yeah

[hollow osprey]

this is the intended way

[gentle lintel]

(i’m too lazy for that either, sorry)

[fallen heath]

:o no worries

so your answer for this is -1?

[gentle lintel]

yea

[fallen heath]

so uhh

[foggy merlin]

$\phi \leq \int f \leq \ksi$

[fallen heath]

I'd like an answer to 2b.

[gentle lintel]

come on

i can’t be bothered to carry out the computations 🤦

[fallen heath]

what's $$\int_0^{10} \abs{f(x)} \dd{x}$$

[gentle lintel]

19 + area of semicircle

19 + 4pi

there

[fallen heath]

:o

well, okie

?

[gentle lintel]

my message

[wraith crypt]

u wot

[fallen heath]

can't read (@_@;)

[dire geode]

poor attitude, honestly

[gentle lintel]

sorry 😦

it got colder here

and i can’t type

or write in a neat way

i mean if you insist, i will

i just don’t want to

[fallen heath]

welp, if that's the case, we can leave at that ig... and here's a trivial assessment to your attitude with calculus:
$$\int 1 \cdot (\ln x)^k \dd{x} = (\int \dd{x}) (\ln x)^k - \int x [(\ln x)^k]' \dd{x}$$

[gentle lintel]

?

so what’s the assessment lol

[hollow osprey]

ansh

wtf is this

wait

[wraith crypt]

?

[hollow osprey]

ah nm

[dire geode]

integration by parts?

[hollow osprey]

i read it wrong

[fallen heath]

my version of IBP is $$\int u\cdot v \dd{x} = \qty(\int u) v - \int \qty(\int u) v' \dd{x}$$

[wraith crypt]

lol

[hollow osprey]

thought he randomly switched order of dx and lnx^k

[dire geode]

Ansh wants to insert as many integral signs as possible in all his formulas

[wraith crypt]

today, integration by parts

[hollow osprey]

then again its almodt 1 am

[gentle lintel]

same

[wraith crypt]

tomorrow, Abel's partial summation

[hollow osprey]

i hav excuse

[foggy merlin]

[dire geode]

Abel's death

[fallen heath]

not really 😑 it's just easier to recognize stuff

at least less confusing than: $$\int u \dd{v} = \ldots$$ or whatever it is

[dire geode]

recognize $\int$tuff

[wraith dagger]

riemann

[hollow osprey]

no one knows

[fallen heath]

Yessir, recognize int stuff

[hollow osprey]

everyone usess DI / tabular

[fallen heath]

i forgot tabular ;-; but it sure is handy

sin^n x [or smth like dat, pardon me]

[hollow osprey]

DI = holy grail

[fallen heath]

so umm 👀

I feel like I made myself pretty clear but, I feel like Chromi's pretty not-comfy with the fundamentals of calculus

[gentle lintel]

so what do i do lol

rewatch some videos?

do more exercises?

[fallen heath]

wait for other assessments [that's just my personal opinion]

[gentle lintel]

that’s a long wait

[gentle lintel]

integrals are just puzzles

[fallen heath]

@dire geode 👀 what do you think?

Also considering every doubt chromi's ever have in last couple days

[dire geode]

probably need to do at least 100 integrals and struggle to identify when to use trig sub, ibp, u-sub, partial fractions

[gentle lintel]

try giving me another one

lol

[fallen heath]

I'd suggest that plus at least a 50-60 decent limit questions, [and a decent fluency with FTC questions]

[dire geode]

additionally, you need to do them to completion on your own

asking for help occasionally is fine

[gentle lintel]

here’s something i tried

[hollow osprey]

https://936933f9-1455-44ce-b414-4d0b35a6c090.filesusr.com/ugd/287ba5_9809e0bcf44548b79263bf7e0c70ad17.pdf

link is super skecth lookin

so theres a picture of it

its BPRP's 100 integrals

https://www.youtube.com/watch?v=dgm4-3-Iv3s&t=69s

[fallen heath]

oops with the number there (@_@;)

[dire geode]

where do i get his wallpaper 😐

[gentle lintel]

i’ve tried those as well

[hollow osprey]

60%?

[dire geode]

what do you mean "tried" ?

[fallen heath]

hmmm

[wraith crypt]

i have looked through all 90 and i have methodologies for about 85 of them in my head offhand

[hollow osprey]

nucleus

[fallen heath]

ntm, there's another set of at least 500+ integrals in my additional sheet

[wraith crypt]

that does not mean i actually tried them

[fallen heath]

which we did as a holiday homework in winter vacation lmfao

so 7 days ✓

[dire geode]

"i've read all the problems and i know either to do: u-sub, trig-sub, ibp, partial fractions, or guess and check. therefore i've tried them all"

[hollow osprey]

this is the best descriptoin

ive ever heard

[dire geode]

,w random number 1-100

[wraith dagger]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by riemann#2529

[gentle lintel]

q2?

[dire geode]

god dammit

[hollow osprey]

LOL

that sucks

[dire geode]

go chromi

[hollow osprey]

chromium

do # 14

[dire geode]

the wolf gods have given you a blessing

less of a blessing

[foggy merlin]

jesus christ

[hollow osprey]

that's the hardest one ive seen so far

[gentle lintel]

harmonic addition formula

[hollow osprey]

(didn't know how to do it immediately)

[foggy merlin]

tf is this ?

[hollow osprey]

wtf is that

[dire geode]

type less, write more

[wraith crypt]

LOL

[hollow osprey]

camil

[dire geode]

latex solutions also welcome

[hollow osprey]

u know what the "harmonic addition formula is"?

,w harmonic addiont ofrmula

[wraith dagger]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by Yottachad#6969

[hollow osprey]

oh god

,w harmonic addition formula

[wraith dagger]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by Yottachad#6969

[hollow osprey]

cringe

[fallen heath]

"You can, for example, never foretell how one integral works, but you can say with precision what an average number will be up to. Individuals vary, but percentages remain constant. So says the statistician" - Sherlock Holmes (censored version)

[wraith crypt]

yes, but it's better known at high school level as the R-formula

[hollow osprey]

BPRP taught me

but would that even help?

[foggy merlin]

ah this shit : acos(x) + bsin(x) = Acos(x+phi)

[hollow osprey]

papa weirstrass

is here to save the day

[fallen heath]

🚶‍♂️

[wraith crypt]

yes that shit

[hollow osprey]

,w integral of (3sin(x)+7cos(x)-6)/(sin(x)+cos(x)+1)

wolfram uses papa weirstrass

[fallen heath]

de le te

[hollow osprey]

no way you can do that with harmonic whatever formula

[fallen heath]

🤦‍♂️

[hollow osprey]

porque del?

[fallen heath]

lmfao

[hollow osprey]

if chromium is workin on that

he isn't being distracted by this

cuz that would take a while

chromium i c you

therefore you are not doing the integral

disappointed

😦

[fallen heath]

Idek if we're done with concluding the $$\lim_{x \to -\infty} \qty(1 + \frac{1}{x})^x = e$$ discussion

[hollow osprey]

yooo

[gentle lintel]

yea

definitely

[hollow osprey]

Chromium prove it via epsilon-delta

then we can be done.

[fallen heath]

:/

[hollow osprey]

no triangle inequality either

[wraith crypt]

(but now you do?)

[hollow osprey]

yes using papa weirstrass

[dire geode]

wait this isn't 1/e ?

[fallen heath]

👀 isn't it just... :whispers:

[fallen heath]

no lmao

[foggy merlin]

hell nah

[hollow osprey]

nah i could see where hes coming from

cuz if you let u = -x

then you would get the 1/-u in the inside

[fallen heath]

yeah lol

[hollow osprey]

and that looks like 1/e.... but its not cuz -u in the power

so whole thing to the power of -1 and then you get 1/(1/e) = e

[fallen heath]

would be more insight-ful if you visited the working of the limit

[dire geode]

"1/e is close enough to e, i understand it enough" --chromi, probably

[gentle lintel]

aha !

tangent half angle substitution!!!!

[foggy merlin]

well cya guys, ima do physics

[hollow osprey]

cya

[fallen heath]

lmfao

[gentle lintel]

(applaud me. or not.)

[fallen heath]

Byee

[hollow osprey]

yes, papa weirstrass

[fallen heath]

illegitim- (coughs)

[gentle lintel]

auhemdnkkekdd

what do.

now

[dire geode]

show your work for 14

[hollow osprey]

$\int \sin(x^2)dx$

[wraith dagger]

Shuri 4 honorable (Yottachad)

[hollow osprey]

"try this" --menace to society

or

$\int \sqrt{1+x^3}dx$

[wraith dagger]

Shuri 4 honorable (Yottachad)

[hollow osprey]

please do not try these

try 41

[gentle lintel]

tangent half angle

[fallen heath]

if you're done with 41. I'll check if there's a more fun one that I seem to recall

[dire geode]

what is your final answer?

you write 3 words down Camil's gonna give you 3 words of her own "what. the. f"

[gentle lintel]

u = x - 1

hmm

[fallen heath]

$$\int \frac{\sqrt{u+2}}{\sqrt{u}} \dd{u}$$ Now what??

[fallen heath]

$\sqrt{u} + \sqrt{2} = \sqrt{u+2}$ maybe?

[fallen heath]

surely ig :o

well, if you're done with this one as well, you're welcome to try: $$\int \sqrt{\frac{x - 3}{2 - x}} \dd{x}$$

[fallen heath]

Let u = x - 3 ?

Let x = 2 \cos^2 \theta ?

have fun :/

[gentle lintel]

jesus

[fallen heath]

I'm amazed you realized. But your current study discipline doesn't depend majorly on your fluency with integrals but rather the basic stuff like how to evaluate a limit, what mistakes to avoid when differentiating/integrating, etc. and mainly the very definitions of couple stuff, and the fundamentals is exactly where I find you lacking.

[gentle lintel]

wdym mistakes to avoid

[fallen heath]

no comment

[hollow osprey]

try this one

[fallen heath]

we're not done with the last three ones ig?

[gentle lintel]

so what have i achieved

in calculus

are you able to provide comment?

[fallen heath]

self-satisfaction

is all

[hollow osprey]

well how to do everything for sure

but prob a little less of the general "ideas" behind the stuff

such as epsilon delta definitoin of limits

riemann sums to derive all the arclength / volume formulas

[gentle lintel]

(i’ve seriously done everything in my power to strengthen the fundamentals, the definitions, and so on.)

(if that’s not enough, i don’t know what is)

[hollow osprey]

i think you've done pretty well my friend

but just look into some of the derivations

[gentle lintel]

(considering how most, i assume, cover these in a matter of weeks)

[hollow osprey]

to get a better grasp

[wraith crypt]

look, maybe i'll give you an anecdote, which so happens to be a true story that happened to me in my very first week of school

so i wanted to test into this advanced calculus class, because it's advanced calculus and i was pretty confident i could take it

famous last words, but that's not the point

[dire geode]

damn ansh, the truth hurts

[wraith crypt]

to study for that test, which i was only told about 24 hours in advance about, i decided to hey let's read and understand limits and derivatives and stuff, and i did that in three hours, covering limits and riemann sums and basic derivatives and FTC

the problem is, i found a mock test after those three hours, and i had exactly zero clue how to do shit

i knew all the definitions and theorems, and that's the problem: that's all i knew

all those little nitty gritty that comes up in the process of solving problems, i didn't have a clue

[gentle lintel]

hey i’ve got an ancedote too

[wraith crypt]

how to write a proper argument for why $\sum \frac{1}{ne^n} < \infty$, no bloody clue

[gentle lintel]

uhh

[wraith dagger]

Camilleone

[wraith crypt]

so i had to spend a lot of time re-learning everything, but this time making sure i did stuff properly, step by step, and that's how i finally learned calculus, properly

[fallen heath]

this anecdote would surely be nice words of caution for me

[soft cloak]

Yeah, there are some things you can only learn in practice

[gentle lintel]

should i share my ancedote lol

[soft cloak]

And at some point you need to get the hang of it

As Ben Finegold once said, theory and practice are the same thing in theory, but not in practice

[gentle lintel]

here, i spent the summer of 2019 attempting all sorts of integral techniques, limit techniques, then i attempted to move on to calc3

yea, waste of time and here i am again

[fallen heath]

Well, what else would you say if you find someone constantly questioning interesting questions, that one would probably not even expect from a, say top rank scorer in hs, only to later find out that this person substitutes x = 0 to find the indeterminate form of (sin x)/x and writes 1/x should have an undefined form?

[gentle lintel]

oh i’ve never said that

or tried things similar

i don’t think i expressed myself correctly

remember that stackexchange thing i sent

that you said was a ‘good finding’

i sent that because i completely agree with the top answer, and if you did agree with the top answer it would be pretty embarrassing, for me at least

and that happened so uhh

[dire geode]

hahahahaha oh shit i remember this

[gentle lintel]

let me clarify picture 1 lol

[fallen heath]

no thanks

[wraith crypt]

oh wow

i must have missed that early part

[soft cloak]

i need context on this

[dire geode]

don't you have like 190 integrals to do?

[gentle lintel]

through direct substitution, if you obtain 0/0, it’s indeterminate (which means whether the limit exists or not cannot be immediately determined)

[dire geode]

you haven't even sent us your answer to

[gentle lintel]

oh yea i’ll try that tonight

[gentle lintel]

this is all

[soft cloak]

Oh that looks like a rancid integral

[gentle lintel]

is it wrong?

[fallen heath]

or to $\int \sqrt{\frac{x+1}{x-1}} \dd{x}$

[fallen heath]

but oh well

[soft cloak]

that also looks like it sucks

[gentle lintel]

if this isn’t wrong, yea it’s just communication problems i believe

[dire geode]

unfortunately for you, communication is important in math

[gentle lintel]

and i’d rather that said instead of a complete lack on fundamentals

[fallen heath]

:/ if I'm not misunderstanding your understandings of the concept, you're mistaken ^^"

[gentle lintel]

yea, engaging in this server helps improving communication

[gentle lintel]

(proceeds to spiral into an infinite loop)

[dire geode]

two things can both be right

[fallen heath]

Like the one fine example I love: $$\frac{\cancel{6}4}{1\cancel{6}} = \frac{4}{1}$$

[fallen heath]

:o

[gentle lintel]

so what’s your verdict

[gentle lintel]

(is this wrong anyway)

[dire geode]

verdict on what?

[gentle lintel]

uhh

‘i need training in computations that’s all’

[fallen heath]

Let's go through this one last time, so I rest in piece

[gentle lintel]

yea, i agree to this

[fallen heath]

I agree to this too.

[dire geode]

you need training in everything

the highest priority is doing problems quickly

[fallen heath]

but I disagree when you use "direct substitution" to explain yourself

[dire geode]

progress wise, i agree with this.

[dire geode]

camil's anecdote should teach you that math is hard and you can't be lazy by skipping doing real work, no matter how tedious you think it is.

[fallen heath]

and that there's a "proper" step by step approach to learning

being all over the place won't help you

[jaunty mural]

[dire geode]

Additionally, this is the coverage for GRE Math Subject. You can't escape tedious calculus if you want to get an advanced math degree

[gentle lintel]

something like this won’t work then, i presume

[jaunty mural]

Assessing yourself...

just grab a paper from somewhere and try it 🤔

Lets see... judging by what youve done I think youve covered the A level/IB syllabus for Calc?

[wraith crypt]

dunno about IB, but technically it's not really A level calc

at least, not the one i took

[jaunty mural]

Ok, I feel like I covered this stuff in IB calc

The further maths calc paper might suit

[wraith crypt]

it's more...bits and pieces of a year 1 sem 1 calc course, i think

[jaunty mural]

He has gone into yr 1 stuff but uh

not gonna be able to do calc questions on those

[wraith crypt]

yeah, that

[fallen heath]

sure you've learnt a bit but I'm concerned you've skipped a lot more important stuff too

maybe it's a nice time to revisiting them basics now... considering you must've practically matured from the pre-calc stage. enough to promote developing your insights into the basics

[gentle lintel]

how can

‘revisiting’ be done

lol

[fallen heath]

:/

[jaunty mural]

For now try look up further math IB calculus past papers

thats where I feel you're at

If you want to gauge yourself

Might be hard to find them hmm

[gentle lintel]

so kinda just

[fallen heath]

Prioritize:

Limits > Continuity > Differentiation > Integration

And if possible, find topic specific papers to help enhance your understandings, the way you've preferred since the start

[gentle lintel]

do them?

-> mastery

(yeY)

[wraith crypt]

i'd say a typical collection of year 1 sem 1 tutorials might work?

because, tutorials

[jaunty mural]

I guess

no idea myself much

[fallen heath]

Camie gonna make a question per day

challenge ur understanding types

[jaunty mural]

Well one thing, I don't think chromium has the speed

because of a lack of familiarity/confidence to apply this stuff

[gentle lintel]

speed of what

[jaunty mural]

doing these Q's

I look back and can guess

[jaunty mural]

.

You guys were doing this earlier right?

If you're confident with integration, this can probably done in 5 mins

Or maybe im pointing at the wrong Q

whichever one you guys were doing

[gentle lintel]

$\int 2^x \sin x \dd x$

[wraith dagger]

Chromium

[gentle lintel]

ibp

[dire geode]

pretty sure 90% of calc students can recognize a product and say "ibp"

[gentle lintel]

,rotate

workings here

,rotate

[fallen heath]

?

[dire geode]

,w integral 2^x sin(x)

[wraith dagger]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by riemann#2529

[fallen heath]

$I(1 + \frac{1}{(\ln 2)^3}) = Y \implies I = (1 + \frac{1}{(\ln 2)^3})Y$?

[gentle lintel]

oh shit

[fallen heath]

Surely... gg

[dire geode]

i'd probably give 8/10 points

oh chromi deleted it

0/10 then

[wraith crypt]

...you could read that?

i don't even know what Y is

[fallen heath]

me neither. it's a 0

[gentle lintel]

yea whatever it's done lol

$\int \sqrt{\frac{x + 1}{x - 1}} \dd x$

[wraith dagger]

Chromium

[gentle lintel]

lmao

,rotate

[jaunty mural]

then finish it off

[dire geode]

what does this even say

[jaunty mural]

Also, you would write working like this in highschool maybe

not at uni

[dire geode]

highschool elementary school maybe
FTFY

[fallen heath]

:o

[jaunty mural]

I'm complaining about a lack of words/direction/explanation

[gentle lintel]

that's technically rough work uh

[dire geode]

technically rough grade 2/10

[fallen heath]

zero

the "trivial" trig-sub was done wrong :o

[gentle lintel]

huh

oh yea

[fallen heath]

sure "oh yea"

Let's see you try something else as well ?

$$\int \sqrt{\frac{x - 3}{2 - x}} \dd{x}$$

[gentle lintel]

becomes integral of secant cubed, i think

[fallen heath]

oh right

$\int \sec^3 x \dd{x}$ is standard, I suppose?

[gentle lintel]

there's a wiki article devoted to it

yea

[jaunty mural]

...

[fallen heath]

well, good luck substituting everything back :o

[jaunty mural]

im out of practice, this would take me about 5-10 mins to figure out. I have no idea how to do it by looking at it rn, but I sure as hell wouldnt rely on a wiki article to do it

[jaunty mural]

like wth is this

theres a wiki article devoted to everything

You should be able to do this on your own hopefully

theres wolfram, why do we need to integrate

you should be able to do this stuff by yourself

[dire geode]

being lazy again

[gentle lintel]

i've done that integral before

so i think i'm qualified to copy from that article

[fallen heath]

yep it's understandable... it really is a common one

[jaunty mural]

if u have done it before

u shouldnt forget it in a hurry

Like at least remember how the integral is done

and then yes, perhaps you can skip it

Parts? substitution?

[gentle lintel]

yea

i remember how

[jaunty mural]

how

[gentle lintel]

parts twice

then set up an equation to solve for the intnegral itself

[jaunty mural]

whats the first split for parts

[gentle lintel]

you get the original integral

[gentle lintel]

sec^2, sec

int the sec^2

[jaunty mural]

ok sure

now in the time you told us, you couldve done it heheh

it looks like a pain, but it rlly isnt

[dire geode]

chromi's too advanced for ansh's problems

[fallen heath]

convinced.. moves forward

[jaunty mural]

You need to be on this level of confidence for algebraic manipulation

[fallen heath]

$$\int \sqrt{\frac{x - 3}{2 - x}} \dd{x}$$

[fallen heath]

ahem

[gentle lintel]

that's $\int \sqrt{\frac{x}{-x-1}} \dd x$

[fallen heath]

excuse me?

[wraith dagger]

Chromium

[gentle lintel]

trig sub should yield sec^2

[dire geode]

do the trig sub

[fallen heath]

,w int sqrt(-x/(x+1)) dx

[wraith dagger]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Ansh#3502

[dire geode]

damn this handwriting is getting worse

[fallen heath]

Is that your answer?

[gentle lintel]

i haven't worked it out yet

[fallen heath]

Also, even wolfram gave the wrong answer to this so ^^"

[dire geode]

1/10

[fallen heath]

please reconsider

[jaunty mural]

im confused how this is concluded

[gentle lintel]

$u = x + 3$

[wraith dagger]

Chromium

[jaunty mural]

dont reuse the same damn letters

[gentle lintel]

it should've been u but sacrificing the holy 'x' isn't worth it

[jaunty mural]

when subbing indefinite integrals

and apparently thats wrong

[dire geode]

i like how by asking us, we're indirectly helping chromi solve problems even though he wants to be assessed

[fallen heath]

.

[jaunty mural]

do u realise you have to sub BACK after ur done with the integral

[gentle lintel]

yea

(alright fine i'll work out the steps.)

[dire geode]

[gentle lintel]

$\int \sqrt{\frac{x - 3}{2 - x}} \dd x =\int \sqrt{\frac{u}{-u-1}} \dd u (u = x + 3)$

are u respond?

[dire geode]

what's wrong with pencil and paper?

[gentle lintel]

formatting

[fallen heath]

handwriting?

[gentle lintel]

triggers my ocd (kinda, i dont have it)

[dire geode]

you can't continue from here?

[gentle lintel]

apparently becomes tan

[fallen heath]

is that virus free? (can I download?)

[fresh geyser]

uh why

its a vid

i made

to watch

bruh

[fresh geyser]

ye ig

if u want

[wraith dagger]

Chromium

[gentle lintel]

$u = -\sec^2 t, du = -2 \sec^2 t \tan t$

[fallen heath]

And what's the trig substitution?

[fresh geyser]

uh a trig substitution is a method for evaluating integrals involving trigonometric functions

[gentle lintel]

ah shit

[wraith dagger]

Chromium

[fallen heath]

ohhh :o I've failed several trig substitutions :c

[fresh geyser]

lol

[gentle lintel]

$-2 \int \sec^2 t \tan t \sqrt{\frac{-\sec^2 t}{\tan^2 t}} \dd t$

[fallen heath]

x = sin t apparently keeps giving me wrong answers in certain scenarios T_T

[wraith dagger]

Chromium

[fallen heath]

sure, use the imaginary number :o

[gentle lintel]

what the fuck

[fallen heath]

oh anyways, once you're done with this one, I'd like you to generalize a substitution for:

$$\int \sqrt{(x - \alpha)(\beta - x)^{\pm 1}} \dd{x}$$

[fallen heath]

Also, what you just did shouldn't have involved any imaginary numbers ^^" please don't joke with integration stuff

[jaunty mural]

I want to see chrom do the 'basic'

1/sqrt(1-x^2) properly

later

[fallen heath]

screams in german

[gentle lintel]

ah yes

[fallen heath]

🏃

[gentle lintel]

range problems, and domain problems

involving the absolue value

history repeats itself

oh yea

sfhsuifhs]fgdfg

fdg

df

g

dfg

[gentle lintel]

arcsin

why did i take so long.

genius

[jaunty mural]

No

Do it by proper substitution

[jaunty mural]

man did i write that shit the wrong way round

I had a good example, but ill have to hunt for it

of where substitution and care are needed

[fallen heath]

👀

[gentle lintel]

(discussing math with shuri while walking through a flower market was honestly one of the best experiences of my life)

[fallen heath]

$\int_0^{\infty} f\qty(x + \frac{1}{x}) \frac{\ln x}{x} \dd{x}$

[gentle lintel]

ok don't

[fallen heath]

?

:/

[gentle lintel]

$u = \ln x, x \dd u = \dd x$

[wraith dagger]

Chromium

[fallen heath]

⁉️

done?

[gentle lintel]

what is f

[fallen heath]

wow

[jaunty mural]

oh nvm i did this integral with you ages ago

when u first learnt sub

[fallen heath]

:o

[gentle lintel]

yea

[tropic oxide]

what problem, if any, is being discussed right now?

[gentle lintel]

this

[tropic oxide]

what is known about f?

[gentle lintel]

i think the final answer is in terms of f and x

[fallen heath]

nothing much really, but it'd be nice to add that "f" is continuous

[tropic oxide]

i mean

with the wrong choice of f, you can and will end up with a divergent integral

[fallen heath]

for example?

[tropic oxide]

f(t) = t

[jaunty mural]

lul

[tropic oxide]

you get int[0, +∞] (x + x^-1) log(x)/x dx

[gentle lintel]

log 🤢

[tropic oxide]

what

do you object to my use of log and not ln to refer to the natural logarithm?

[fallen heath]

,w integrate (x + 1/x) (ln x)/x dx from 0 to infty

[wraith dagger]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Ansh#3502

[tropic oxide]

told you

[gentle lintel]

how did you know it diverges (nice comparison test exercise)

[tropic oxide]

the integrand behaves as log(x) at infinity

[fallen heath]

$f(x) \neq f(1/x)$ works?

[tropic oxide]

works in what sense?

this condition doesn't at all guarantee that the integral converges

say, where'd this problem come from anyway?

[fallen heath]

my module :o

[tropic oxide]

can you show its original statement there

i want to see it

cause i'm growing more than slightly suspicious of how you're presenting it

[gentle lintel]

$\int^{\infty}_0 x f \qty(e^x + \frac{1}{e^x}) \ \dd x$ is a pretty neat form i obtained

[wraith dagger]

Chromium

[fallen heath]

$I = \int_0^{\infty} f\qty(x + \frac{1}{x}) \frac{\ln x}{x} \dd{x}$ \ $$= \int_{\infty}^0 f\qty(\frac{1}{x} + x) \frac{x\ln x}{x^2} \dd{x}$$

[tropic oxide]

you're not answering my question, ansh

do you or do you not have a picture of the problem as it was originally stated in your module?

[fallen heath]

I do

[tropic oxide]

okay then would you please be so kind as to send it here

[fallen heath]

x -> 1/x was the intended substitution, I presume

[jaunty mural]

looks like its D lul

[fallen heath]

Also, the answer was A)

[tropic oxide]

is nothing at all known about f?

[gentle lintel]

huh

i don’t get it

[tropic oxide]

ok, hold on

we can let x := e^t

[jaunty mural]

x -> -x sub

[tropic oxide]

then the integral becomes $\int_{-\infty}^{\infty} t f(e^t + e^{-t}) \dd{t}$

[wraith dagger]

Ann

[gentle lintel]

not 0?

[tropic oxide]

which, assuming that f behaves nicely enough at infinity, would be 0 as the integral of an odd function over a symmetric interval.

but unless we know that f does indeed behave nicely at infinity (or even not at infinity - who knows, maybe it's so nasty it's non-integrable!), and the integral does converge (which, again, we aren't given),

we cannot say this integral even makes sense let alone converges

[fallen heath]

since the module was meant as a discussion for class... I'm certain sir discussed this through

of course it would be up to the student to notice such details, is why I planned to bring this up as a matter of subtlety when doing integration

[gentle lintel]

not f(-x - 1/x) ln(-x)/x [inf, 0]??

[fallen heath]

x -> 1/x brilliantly gives the answer 0, but does it?

[jaunty mural]

idk, im not paying 100% attention. Ansh what sorcery is this

[fallen heath]

you advised x -> -x substitution lol

[jaunty mural]

oh nvm im blind

[fallen heath]

that's what chromi did

[jaunty mural]

x -> 1/x

[gentle lintel]

i did u = ln x

effectively leads nowhere

[fallen heath]

Yeah. I figured

$= -I \implies I = 0$

[fallen heath]

but as Ann mentioned, this depends on what's up with f(x) :o

ntm, you're also meant to assume that "I" is finite, to be able to play with the limit

[fallen heath]

btw, in case you're lost, the topic of discussion was Chromium's assessment on calculus... and having had discussions with Chromium on several occasions, I felt like revisiting the basics via questions would be the optimal choice for him before moving on to Linear Algebra for multivar

[tropic oxide]

you don't really need calc directly for linear algebra

[fallen heath]

Linear Algebra for multivariable calc-

If I'm interpreting correctly, Chromium's intention is to proceed with multivariable calculus(!?)

the assessment is (probably) intended to gauge his understandings and if it's fine to move on.

[gentle lintel]

so kinda do more questions

-> ok?

https://www.ibo.org/contentassets/7f6c7681e0b34fc8b0541c1229c7521d/gp5_mathssl2.pdf
perhaps i should try this

ib further maths calculus past paper, as shuri suggested

[fallen heath]

vectors / matrices?

[gentle lintel]

2, 3

q2, 3

not 1 4 5

bad

wait ynw, this is too simple

[fallen heath]

Just chill and devote yourself to questions for a while. Prioritize the order LCD(limit -> continuity -> differentiability), then Integration and do stuff accordingly, step by step, until you're able to properly arrive to the answer at least 7 out of 10 times