the first 5 days of calculus 2 but the integrals get harder!

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Today we will see what your first 5 days in your calculus 2 or AP calculus BC class is like. Calculus 2 is known as integral calculus and we usually start with learning all the integration techniques. We will cover the integral of x^2 with the reverse power rule, the integral of x*e^(x^2) with u-substitution, the integral of x^2*e^x with integration by parts, the integration of sqrt(1+x^2) with trigonometric substitution, and the integration of (2x+1)/(x^2+3x+2) with partial fraction decomposition.
0:00 day 1, reverse power rule
0:20 day 2, u sub
1:27 day 3, integration by parts
2:29 day 4, trig sub
6:16 day 5, partial fraction decomposition
8:51 Check out Brilliant
🛍 Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
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Thank you all!

[@blackpenredpen]

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[@MiroslavOstapenko]

3:05 Shouldn't the sec²-1 = ctan²? Im not very used to sec notation as we don't use in in my university, but as I understand you divided all by sin² then cos²/sin² will give us ctan² Regardless if you see this comment or not, I appreciate your videos, they are the best!❤️

[@defect8352]

Your 100 integrals part 1 helped me so much. I am beginner in calculus 2. Really helped me a lot. Now I am surprised I can do most of the integrals (that are doable) by myself. Keep up the good work man.

[@AyberkDurgut]

You know there is something serious when he has 2 pencils.

[@whhitryjekugitihg]

he always uses 2 pens

[@aarondelgado3421]

Pencils? He uses dry ease markers.

[@Bruh-bk6yo]

Serious is when the purple marker joins the fight.

[@user-xk4uz8fg7t]

Blackpen Redpen :^

[@scareflare7553]

​@@Bruh-bk6yo purple marker is serious mode, no problem escapes..

[@jokerdark3110]

Hey king ! U dropped this 👑 I got my 20/20 in math bc of u ... I always make my teacher be like 🗿 with ur methods Tysm💗

[@MarceloKatayama]

An interesting fact is that the integral used for day 4 is one you can use to define the area under the curve of the upper half of the hyperbola. This, in turn, can be used to define the hyperbolic functions in exponential form i.e. sinh(x)=(e^x-e^-x)/2. Additionally, the same steps can be used to derive Euler's formula by using some imaginary number manipulation on the radicals.

[@highlights973]

I recently finished university in Computer science and i came back to this channel today to say Thank you so much for helping me in Advanced Mathematics during high school God bless you Brother

[@user-gs6lp9ko1c]

Hmm, I seem to remember trig substitution taking more than one day to master in my Calc 2 class... Great job! 🙂

[@21pandas71]

thanks for the review, i really love your videos!

[@franzdeofrancisco2154]

Passed cal 2 because of you, now taking DE. Thanks man! 🔥

[@GrandAdmiralMitthrawnuruodo]

That‘s like the last year of Highschool. I actually used partial fraction for my Maturapaper (Switzerland). Great stuff!

[@ahmedyacine5661]

Even when you do a fun video I learn something new from it❤

[@cleopasmuchiri]

So helpful and good vibes

[@DefenderTerrarian]

I'm about 3 weeks(12 days) into Calc 2, they haven't taught us that last thing. Also, that integration by parts is so much easier than the way I was taught.

[@thatomofolo452]

Straight up Fax 💯

[@jerhere5251]

Can you make a video on the branches of the Lambert W function please ?

[@giuliogiacomelli6667]

Can you explain the transform of Fourier? With some exercise

[@dhvanitmehta5490]

Sir I am a great fan of yours

[@matthewgeary1811]

that integration by parts method was INSANE

[@Wandering_Horse]

I bought Euler's number 2.718 t-shirt from your store, gotta admit I can't wait to wear it to class. 😅

[@bjornfeuerbacher5514]

In my lessons, I always do partial fractions first (after the initial easy integrals), then partial integration, then u sub. I think partial fractions actually is the easiest method, you can always do it the same way; for partial integration and u sub, you often have to guess and check how to actually apply the method.

[@devanzummallen5677]

Can you continue this? I'm currently taking Calculus II and I'm curious to see what is yet to come later on. I just finished learning about Day 5 for this video last week.

[@savage_cat5172]

Polar coordinates and parameterization for the most part

[@christopherpoulton8973]

Sequences and series

[@fabicastillobb]

in my university, our teachers taught us that in parcial fraccions we multiply and distribute the bottom, so it cancels every Coeficient with their own bottom. and if we have A/(x-x1) + B/(x-x2) = top part / bottom we multiply the bottom so to get A*(x-x2) + B*(x-x1) = top part is a method more stright

[@jamie31415]

That's the usual method, this is just a shortcut that works in most cases.

[@ozreb21]

Yo I'm taking calc 3 but I didn't know the cool way u used to calculate that integral by parts, I was taught a much worse formula! Thank you

[@lucas-hadukas]

You are one of the mathematicians I enjoy watching the most, also, what size tablet do you have?

[@blackpenredpen]

Tablet?

[@moonwalkhi]

i think he means whiteboard@@blackpenredpen

[@Allahu_Akbar_the_one]

Unpopular opinion: Calculus 2 is much easier than Calculus 1. I truly believe in that statement!

[@syfx1485]

An unpopular opinion indeed. Maybe you studied really hard for Calc 1 and did really well, so you were overqualified by the time Calc 2 comes?

[@sebas31415]

I am only a softmore in high school and this makes sense to me

[@mcalkis5771]

We're slowly getting closer to calc 3.

[@atzuras]

day 1 ok day 2 ok day 3 ok day 5 ok day 4 let's hope it's not on the test.

[@yanntal954]

That's way different than my Calc 2, way less definitions (Darboux integral, Riemann integral), (even more) limit proofs, uniform convergence and when you can swap sums and integrals, when you can use the fundamental theorem etc., Taylor series and many more. If there is time they sometimes also teach either double integration and some introduction to calc 3 or even a bit of Fourier analysis.

[@MusicalInquisit]

Curious: are you French?

[@yanntal954]

@@MusicalInquisit I actually am

[@bjornfeuerbacher5514]

As far as I know, the more abstract stuff (definitions, limit proofs etc.) is taught in the USA in lectures called "Real Analysis", not in Calculus.

[@humhum3987]

hey blackpenredpen i'm a math student, and I was practicing some exercises I'd imagined, when I asked myself a question to which I searched for an answer for over half an hour before giving up. I was wondering about the value of the integral from 0 to pi/2 of 1/sqrt(sinx). I looked at the solution at Wolframalpha, which is 2sqrt(pi)*Gamma(5/4)/Gamma(3/4). This number can be written as - Beta(-1/2;5/4), where Beta is an Euler's special function. This result is related to elliptic integrals in so far that this integral equals F( phi | k² ), with F( phi | k² ) is an incomplet integral of the first kind, phi = pi/2 and k² = -1. Elliptic integrals are a field we've never studied in class. Do you think you could do a video about this integral ? thank you very much for your time and your effort teaching us about integrals

[@heinrich.hitzinger]

🍔

[@at7388]

Please make a video about the i-th root of i. Thank you.

[@blackpenredpen]

I have done that one already.

[@at7388]

@@blackpenredpen Thx I have found.

[@warwick802]

"Dont forget the +C brings so much nostalgia lol"

[@mtrichie111]

"I know thats just bad teaching but whatever" HAHA, Love this guy !!!

[@yokoyapen]

4:01 suddenly it changes, the x and dx

[@jmooroof1769]

so accurate; they just show you how to solve the problem but you don't know what the hell is happening 🤣

[@projektaquarius]

Literally day 2 is what broke me. I am lucky I got a C.

[@Mawyman2316]

All these years and he still refuses to clip the mic to his shirt

[@Plasmacticus]

five nights at calc 2

[@umertaiyab5500]

can anyone explain to me why the ans to the differentiation of (x^3*y^3=4) different from (y^3=4/x^3). when i have just moved the x^3 term to the righr hand side.

[@bjornfeuerbacher5514]

The answer is the same, if you do it the right way. Differentiating x^3*y^3 = 4 gives 3 x^2 y^3 + 3 x^3 y^2 dy/dx = 0 and hence dy/dx = -y/x. Differentiating y^3 = 4/x^3 gives 3 y^2 dy/dx = -12/x^4 and hence dy/dx = -4/(x^4 y^2). Looks different at first sight. But when you plug x^3*y^3=4 into the second solution, you'll see that this is exactly the same as the first one.

[@amiram7865]

Wish doesn't have to demonstrate all calculus in my college

[@terkapak]

ln(y)=ln(a-2x) what is the derivative of ln(y) with respect to ln(x) Note: not with respect to x, but with respect to ln(x)

[@bjornfeuerbacher5514]

d(ln(x)) = dx/x, and hence d/d(ln(x)) = x d/dx, so the derivative with respect to ln(x) is x times the derivative with respect to x.

[@theplant4046]

The thumbnail tricked me i thought it was pice of hair instead of arrow pointing at him

[@blackpenredpen]

Wait. I forgot to remove that when I was making the thumbnail 😆

[@maxhagenauer24]

That's day 1? I learned U sub and integration by parts on my first day of calc 2.

[@herbcruz4697]

I learned u-substitution toward the end of Calc 1.

[@richiewitkowski7142]

Man, I am starting week 5 Calculus 2 right now and we have not learned ANYTHING from day 3, 4, or 5. Day 3 and Day 5 looks so useful right now for some of the stuff I see already. We probably arent allowed to do those methods because we havent been taught it yet. In Calc 1, someone used L'Hopitals Rule before we were taught it and gave him a 0 for the question

[@PwnMe100]

ronald?

[@eddcs1901]

That's more like 2 months of Calculus 2 for me, Don't worry you'll get there. And the part about using l'hopital's rule before learning it is so familiar lol I remember I used it on an mcq test once.

[@sajeucettefoistunevaspasme]

what if he prooves it then uses it ?

[@nonameuntilifindanewone.6053]

May I ask a question I've been confused in?

[@AaluBabu]

You know math’s hardcore when it feels like English grammar

[@artophile7777]

Yo!

[@PankajYadav-zb4vv]

Hi sir, I am an Indian, I am very big fan of you, I love mathmetics, do you read me higher mathmetics for Olympiad plz tell me, I see your all videos your very intelligent person

[@nginborin]

I like you

[@capnbug]

My first 5 days were all just review lol.

[@AL.mNeSK_511]

I am the first 💪💪💪💪

[@suryanarayankumar7986]

Don't miss any corner of mathematics.

[@j.blancof2605]

tal cuál XD

[@zhabiboss]

“I know that’s bad teaching but whatever” 💀

[@vbacz]

Man im in day 3 and im starting to get humbled by math

[@michaelleue7594]

I really don't love the approaches you're taking here. There are a lot of shortcuts that are memorizable but that don't actually help people understand. They're the kind of techniques that are great if your goal is to actually compute an answer, but are absolutely awful for getting students to comprehend the shape of the underlying concepts. If educators expected students to need to compute integrals by hand in real life, knowing shortcuts would be great, but we don't. We just want them to be able to look at a problem and go "I understand enough about this to be able to map out the steps to a solution" and giant distracting shortcuts that short circuit the instructional power of the example are therefore a problem.

[@Twi_543]

Lost my silly brain on day 2

[@arnaldosantoro6812]

On day 4 people dies

[@asulator3146]

You didn't age at all in 4 years

[@sebas31415]

???

[@Gg-ij7li]

Jesus loves you all and wants to free you from any shackles in your life! Call upon His name and He will save you! If you confess with your mouth “Jesus is Lord” and believe that He rose from the dead and abandon your sins, you will be saved! God bless you, have an awesome day ❤

[@MathFromAlphaToOmega]

But can he help me evaluate difficult integrals?

[@ahmedyacine5661]

It's not a religious video

[@Sortiara]

You need to calm down, sir.

[@want-diversecontent3887]

What's the integral of 1/(Jesus+ln(Jesus^2))

[@robertveith6383]

​@@ahmedyacine5661 -- It might help if you or anyone else would click on the far right on the vertical three dots to report the OP's post under spam.

[@tobybartels8426]

You skipped the day where you learn to do cos⁴ etc.