Integration and the fundamental theorem of calculus | Chapter 8, Essence of calculus

[@johnhammer8668]

How cruel it was to learn calculus for years in school and college without knowing the fundamentals. Glad the dark ages of pre internet era is gone. Thanks so much for this videos. You are a gift to mankind.

[@Void_Knight]

A sad tale indeed but we shall no longer be in the darkness but in light Thnx to the magicians of KZbin

[@maxwellpineiro]

indeed so thankful for the internet lol

[@acatisfinetoo3018]

Blessed be the internet for it's bestowing of knowledge...

[@mcsyllesen5183]

Yea, i remember doing this in 7th grade. It wasn't so bad tho

[@circuitman8792]

And yet I throw away my valuable time in school when I can simply learn without pressure from books and the internet. But no, monopolies hold so much influence over the education system, changing the education system would be the equivalent of those monopolies loosing millions. I guess I have to force myself to "learn" in a monotonous curriculum that was designed by the school district in order for me to regurgitate information and throw it up on a test.

[@RobertMcHalffey]

This channel, The Organic Chemistry Tutor, and Khan Academy are currently giving me the tools to master integral calculus... for free. What a wild time to be alive.

[@viscid2906]

oversimplified reference?

[@rohankodibagkar2552]

Don't forget blackpenredpen!

[@thephilosophyofhorror]

It's awesome ^^

[@nikolatezzla3894]

Definitely great channels

[@muradpetrosyan5128]

Professor Leonard also

[@theflamingsword]

Schools should just adopt this as an intro video and along with some worksheets the lectures can take two weeks off.

[@ChristGodinyouItrust]

Haha, he is really really good.

[@RaghavaIndra]

lol absolutely how it should be.

[@iReachevo]

In my Calculus cource it is actually recommended to watch this video series

[@FrenchcoreFlava]

then the lecturers don't improve as teachers. Usually they're there to get better at their job and make more money by having successful students with their own content

[@tessacarstairs5998]

My school has already!

[@nikoyochum6974]

Wish these videos existed when I was first learning calculus :P

[@Metalhammer1993]

yeah i never got where that area business came from. i just accepted it and memorised the rules. and got done with it. i knew the area was used to discover some integrals. like 1/x well if we used the 1/alpha rule we´d get 1/0*1 (as x to the zeroth power would be 1) and that is utter nonsense first it would be a constant no function second it´s literal physical pain for everyone with a bit (even my mini mini mini bit) of mathematical understanding. 1/0 that hurts. does that mean yo ucan´t integrate it? looks like it right? but i think Leibniz (might be wrong here though) found that the Area under the curve grew logarithmically. setting up the real butt saver S 1/x dx=lnx . but i always just accepted "okay the integral is magically bound to the Area under the curve".

[@carlosalbertolopezreyes4424]

My calculus class in the school is dull, i'm lucky to learn very important things here and Mathologer channel

[@iMiilk182]

Carlos Alberto López Reyes thanks for the mathologer tip :) didn't knew the channel

[@geekyprogrammer4831]

ikr!

[@IsaacC20]

That's because most math teachers aren't programmers who can utilize animation

[@shubhamshinde3593]

Best 10 days in the life of KZbin!!!

[@N0Xa880iUL]

Shubham Shinde agreed!!!!

[@sanjeevkushwaha7614]

Yes I agree.

[@Shockszzbyyous]

Shubham Shinde hell yea

[@tubatm]

I agree to.

[@vbmendrot1]

Since the series started, everyday I wake up that's the first thing I do. It's so good to watch it

[@3blue1brown]

Next up is a different perspective on why the area under one graph is related to the slope of another. Full playlist at kzbin.info/aero/PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

[@mihaiplacinta5307]

Please do a vid on stochastic integration

[@tims2532]

I second that! Since the video where the derivative of x^2 was done using a sqare with the tiny (dx)^2 part vanishing, i had wanted to see something on quadratic variation. :D

[@xelaxander]

3Blue1Brown Thumps up for stochastics. It's like mating calculus with a massive application for it. Beautiful!

[@MrL314]

Is there a way you can explain concavity and the second derivative in an intuitive sense?

[@rogerab1792]

It will also be awesome if you made a series about probability

[@prawnydagrate]

I'm just a 12-year-old in 8th grade who likes math and this series so far has fascinated me and I love how these videos won't end without providing a full understanding of what's taught. This series is amazing.

[@Matthias27182]

Please keep learning math for as long as it fascinates you.

[@tahabashir9405]

This kid is a rare one. I was not even fully conscious at 12. lol

[@user-mv4ix7jd8o]

I'm 15 and also learning it! Wanna chat?

[@prawnydagrate]

@@user-mv4ix7jd8o Uh sure ig

[@prawnydagrate]

@@Matthias27182 Lmao it only took a few weeks for me to get into chess and forget about math

[@joseleperez8742]

Hey, I see lots of comments wishing they had this in their school days and, know what? I'm in my school days!!!!! I'm taking a lot of advantage of this series, THANK YOU!!!

[@harikumarv4658]

Happy Mathin'

[@bariumselenided5152]

I’m so lucky that my calc professor seems to have the same love you do for teaching why things work the way they do, not just teaching how to do problems. His classes are always as engaging to me as your videos. I honestly can’t wait for calc 2 in fall with him.

[@ahmxdhsn]

seriously man... A good teacher can make you love the subject even if you never knew about it before That professor of yours is a man of great value! I think you should give him a gift if you can.. i think he deserves it!

[@skatelife59]

I'm currently studying mechanical engineering and working as a tutor. I have to say, this series is absolutely amazing! I can only imagine how easier these concepts would have been to grasp if it were to watch your series when I first started learning calculus. I might just incorporate some of your notions in my tutoring sessions, if you don't mind!

[@robertegwu8551]

M studying mathematics in college at the moment.. This videos n its execution has been helping me with the gaps in my knowledge

[@squibble311]

why is your profile pic euler

[@ostapigor1607]

@@squibble311 why not>>>???

[@rahimeozsoy4244]

@@ostapigor1607 Gauss is better

[@squeakybunny2776]

@@rahimeozsoy4244 dude sssshhh you wanna start a war in here?!

[@samuelkorger3567]

When I was in undergrad, educational videos on KZbin were really in their nascency. Having access to this, Khan Academy, and organic chemistry tutor would have been a game changer. It’s wonderful to see that future generations will have access to such an efficient form of learning.

[@kjekelle96]

0:00 intro 0:55 distance from velocity 2:27 area under a graph 4:08 approximating and refining 6:29 writing an expression: the integral of v(t) 8:30 how does this help? 9:34 the area as derivative 11:17 the antiderivative 14:57 the fundamental theorem of calculus 16:18 recap 17:46 signed area 18:55 outro & sponsor

[@pableraspfgpfg468]

Great explanation. I am an aeronautic engineer that loves calculus but until now, it had been quite difficult for me to deeply understand why the integral is the "antiderivative" of a function. Thank you for your great work!

[@rikitobruece2386]

I still don't understand why integral is the opposite of derivative, could you please explain what you understood? Thank you

[@happysoul5031]

@@rikitobruece2386 I hope I can aid to your understanding, although it's been 2 weeks since you posted. You can imagine the integral to be the "sum" of all the tiny strips that an area under the curve has been broken down into. The caveat is that you must remember that the integral is not just the sum of all area strips, it is the sum of the strips as these strips approach zero width. That's why integral is different than the ordinary sum. Why is it opposite to the derivative? Let's say you have the information on the distance travelled by a car with respect to time,and you want to find the velocity of the car during that time interval. You would use the derivative of that distance versus time function. Now reverse the situation. Suppose it so happens that you have absolutely no data about the distance your car has travelled, but you just have access to the speedometer(i.e. velocity). You intend to find the distance travelled by your car through this data of velocity versus time. Earlier, you had distance versus time and you found velocity by taking the derivative. Now, when you have velocity versus time, and you want to find the distance, you would take the "integral" of the velocity data. So in these two situations, you seek to find the derivative of a given function, and in the next situation, you already have the "derivative"(in the form of velocity data from speedometer), and you need to find the function which has this derivative(distance). This is called integral.

[@rikitobruece2386]

@@happysoul5031 Thank you so much for taking out your time. I have understood it well!!

[@indian_otaku2388]

@@lollel1490 Basically that's what I think will happen. I suck at calculus though so don't blame me if I'm wrong 😂😂😂. I used to hate calculus until i watched 3Blue1Brown videos now it's getting interesting.

[@Caspar__]

I have watched this video 4 years ago, while I was in 9th grade and now I am studing math at university and watching it again. What a journey

[@exposingreality6391]

Wow, you studied this in 9th grade at s hool or you were just interested in math?

[@Caspar__]

@@exposingreality6391 I was just interested in mathematics. I knew some people who where way older than me and they carried me along.

[@piraloco5864]

@@Caspar__ im 13 lol

[@chrismain7472]

I love that the gradient of the area rectangles animated the idea of smoothness. When there are 8 large rectangles, each rectangle's color is noticeably different from the color of the adjacent rectangle. As the rectangles get smaller (approaching the area under the curve) the colors approach a smooth gradient as well. It seems that beautiful and subtle tricks are your forté, and this one is no exception. Thank you for your very helpful videos!

[@tim40gabby25]

Nice spot. Should be developed.

[@FacultyofKhan]

On a more serious note, these videos are very well done. It's great to see the fundamentals (huehuehue) of mathematics being explained in such an intuitive manner. I think I could use your videos to help my own content, which is mostly geared towards higher-level undergrad/graduate science/math. If I incorporate animations and an intuitive angle, I imagine the explanations I give could get even better. Thank you for making these lessons! - Faculty of Khan

[@HenryNguyenReee]

This series is a perfect supplement to the Khan Academy curriculum or any school curriculum, which just teaches the "rules" of calculus.

[@cblse]

Faculty of Khan

[@xanokothe]

huehuehue? BR?

[@wedeldylan]

David Valero ah fuck, you got me :'(

[@abdullahumar6685]

Faculty of Khan i

[@FacultyofKhan]

Friday ... check Little or no work to do ... check 3blue1brown uploads a video ... check Today is a good day!

[@julianha5473]

Faculty of Khan same, except for the work to do :(

[@oliverhees4076]

neglecting to do my geometry homework now to watch a calculus video

[@graciouscompetentdwarfrabbit]

I should be studying analytic geometry, conic sections, to be exact... but screw it, right?! i shouldn't be doing it..

[@proto9053]

Oliver Hees But Geometry is also interesting... that is if the subject is taught as pure mathematics.

[@h.l.69]

I'm not sure about the day ... check "I should not be wasting time on writing this comment" amount of work left to do ... check What was the last one, ok I have to go. ... check Someday will be a good day!

[@yoavmatia]

this is THE MOST succinct explanation i have ever heard for integrals - as a teacher myself , I tip my hat to you, very well done!

[@metrictensor9745]

I've been watching you for ages and JUST realised that this "group of pi monsters" is made up of 3 Blue and 1 Brown pi monsters....

[@abelpalmer552]

Just realized that from reading this comment.

[@realMuskDonald]

you are not the last

[@neongamerlp9856]

ur right

[@matthewhazaras6143]

I never noticed that

[@Chopinwannabe7556]

I thought 3 blue 1 brown was a reference to alleles and genes.

[@Metalface123]

Been studying calculus for a semester, without any motivation. Now, I found joy in doing it, and I really enjoy your videos. Inspires me to do more work, and it drives me to try to be more creative with it. Thanks!

[@ThatGuyDownInThe]

being in a car and only looking at the speedometer sounds incredibly dangerous

[@technux5382]

you think outside the box

[@alexandertownsend3291]

Not if you are a passenger.

[@aurelia8028]

sigh... *rolls eyes* whatever dude

[@danielcheung9920]

and then when u go backward

[@randomguy263]

Well, if the speedometer shows 0 you should be alright. Assuming it isn't broken, of course.

[@reesespieces5386]

I’m a first year Math student and I have to say, your channel is the reason I love math so much. It’s part of the reason I decided to study it. It hurts when I hear people complain about math when they’ve only been taught how to do things instead of why you do it that way. However, the hope that they might discover your videos keeps my head held high. Thank you for these “Essence of” videos. They help me to understand the ideas behind what I’m learning. I’m grateful that my profs do go into some detail as to why things are the way that they are. But when they don’t, you’re there to give me the intuition behind the math. I could never thank you enough for these videos.

[@connorduffy7964]

I'm in my final year of highschool taking calculus right now and these videos have proven invaluable to my understanding. my favourite part about math is when it finally clicks, and your videos are making it click. i'm at a point in my eductation where I can't just coast through because the material is actually becoming challenging, so you are like a bridge between what my school can teach me and what I want to know. i cannot thank you enough

[@Stoic_Persistence]

Man, the way you teach intuition in math is so beautiful. I wish we had a 3Blue1Brown in every subject.

[@FrostyAUT]

School: You gotta learn this. Me: Why? School: You gotta learn this. Me: But what is it good for? School: You gotta learn this. A few years later in university ... Me: Geee, I wonder how I can calculate the area under that curve so I can get the consumer surplus from non-linear demand and supply functions ...

[@mamandroid]

Are you at the AUT Uni? Btw what you say is relatable.

[@kbolternorris2676]

you could argue with a highschooler that they should learn it because building up the capacity to think in abstract of students is overall good for society but what's the point man, teens are morons and won't really care

[@tomasito6417]

I’m actually in algebra 2 right now but taught myself precalc in one day and am now getting into calc. So far I’ve done a lot of anti derivatives, derivatives, and integrals. Pretty cool stuff I just came here to be given a picture and practice whatever problems he put on the screen. Pretty good examples honestly

[@edmarx2325]

​@MrComrade I'ts actually opposite. Everyone ABOVE 25 y.o. is a complete moron and thus needs to be eliminated.

[@christophernicolaides7793]

@@tomasito6417 SAME. LITERALLY. I’m doing all of precalc today while starting to do calc in algebra II

[@BootesVoidPointer]

This is the most beautiful series I have ever seen in my life.

[@scipio42]

I cannot describe how much I love this series. I watched it once when I started learning calculus and enjoyed it a fair bit. But now that I can really appreciate the subtleness that it shows and the nuance it gives, it's even better!

[@gregofuente1119]

Grant is the Richard Feynman of KZbin

[@adhithasimhanraghavan7516]

Totally

[@JohannSuarez]

Couldn't agree more. He's an exceptional teacher!

[@squibble311]

never heared a more appropriate comparison before

[@albertmendoza1468]

Exactly!

[@GeorgePlaten]

If you mean that you think you understand everything when following along but half an hour afterwards you haven't got a clue about anything, then yeah. Just like Feyman.

[@guloguloguy]

WOW!!!!! THESE ANIMATED GRAPHICS REALLY DO HELP IN TRYING TO CLEARLY "VISUALIZE" WHAT IT IS THAT YOU ARE EXPLAINING!!! "BRAVO!!!" THANK YOU!!!!!

[@MrMineHeads.]

I LIKE IT TO, BUT WHY ARE WE SHOUTING?!

[@jibran8410]

This is my favourite series as of now.

[@reubendesilva]

This series on calculus was my first introduction to the subject when I was exploring it for myself before learning it in school, so when I came to studying it, I actually had an idea of how to solve different and interesting problems because these videos taught me why they work and more generally the theory of the subject, rather than blindly applying high school formuals to solve homework and exam problems. This series in particular is what first truly lit up my love for mathematics, and I cannot thank this series and channel enough. This is what schools need: giving children the ability to be understand why the maths works, and I believe it would really make more students grow a love for the subject, as it is not just memorisation, but derivable logic. Thank you Grant, and never stop sharing your love of maths with us!

[@venkatesansankaranarayanan6101]

What a fantastic video! I was just getting into integration in school and finding it tricky, but this video made it become so much more intuitive. Thank you so much for making these wonderful videos!

[@Claramoo]

You are one of the main reasons why I loved math in the first place. Thank you so much for showing me this beautiful subject that not many people I know enjoy it.

[@SoumilSahu]

FIRST! and also, this the THE BEST CALCULUS SERIES ON KZbin for beginners!!

[@azzarooni8532]

Not only for beginners. For those like me that have already learned calculus but want a better understanding find this incredibly helpful

[@ASLUHLUHC3]

*For anyone

[@geekyprogrammer4831]

well, I have done calculus 4 years ago during my undergraduate years! And overall I am good at Calculus. Still this video was amazing for me as there were many new things I didnt knew he explained :)

[@squeakybunny2776]

@@geekyprogrammer4831 can you give an example what you learned here that you didn't know yet?

[@harikumarv4658]

@@squeakybunny2776 I'd suppose the abstract intuition that you might realize while watching Grant do his bid. As a grad student, I sometimes just come back here just to witness the fundamentals being explained by him as it incites a cloud of imagination in my mind and lets me rethink the problem from an entirely different standpoint. Most of the time, it's more like I'll just be overthinking without considering the concrete fundamentals.

[@davidyim5019]

I don't know how many times I have watched the series but I finally understood what calculus is about. I would have never understood the theorum of calculus if I tried to learn from the textbook without animation. Thank you very much!!

[@cd-777]

9:37 - 11:25 my favorite part, this will be super helpful for beginners of calculus to understand the whole idea. Good video.

[@philipbraatz1948]

I believe that you are the number one math youtube

[@gautamchettiar4150]

Yep he's quite cognizant

[@isexactly383]

I've just had a double lesson in economics... This is exactly the right thing to calm you down.

[@U014B]

J&M Productions Right? Economics is a branch of Mathematics in the same way Astrology is a branch of Science.

[@eulefranz944]

loooooool !!! :DDD

[@xelaxander]

J&M Productions Maths Bachelor here. I can only applaud.

[@fossilfighters101]

+

[@NoNameAtAll2]

+Noel Goetowski well, at liest economics counts right

[@zack_120]

Genius to use car velocity as the f(x) to demonstrate the principle of integration, making the understanding of the subject very intuitive and precise. Again, 3B1B is the best animated math video channel that makes the learning of math a breeze and very enjoyable. Soooo unique! Thank you very much !!

[@School-um6ck]

7:28 For anyone else wondering, there is a way to be 100% accurate when finding the area under the curve. You need to find the antiderivative and then you can use it as is, or plug in the needed numbers. For some functions it might be easy, like 2x is just x^2. For others it might not be as easy, or reasonable, but it is possible for all of them.

[@supreethbhaskar3405]

at 7:02, not only it a factor in each quantity that we are adding up it also indicates the spacing between each sample step. wow that is at the height of Grant's explanation. Really appreciate it.

[@atharvagarwal6412]

0:18 to 0:31 this is what people should realise about math! So well said and relatable!!

[@mrnicomedes]

Holy moley! An interrobang! Your visualizations are absolutely superb, and you've got a great radio voice. And your videos are fantastic in laying bare the underlying structure, simplicity, and beauty of mathematical reasoning. Thanks!

[@Battmatt99]

as an undergrad student who is struggling in calc, thanks so very much for these videos. they're very very good!

[@mannykhan7752]

After 28 years, re-learning Maths is so much fun. Wish we had these animation and videos to help us back then.

[@sebastiangudino9377]

I first encountered the integral by accident years ago, when i was a kid and i said "I want to make a game". To make a character move, when you press a key, you make the key press add as an speed (Or an acceleration) to the character, then a mainloop/update function takes the character object, and takes the acceleration and add it to the speed, then you take the speed and add it to the position. And you then maybe multiply by the delay of a frame (The inverse of the framerate) That made a lot of sense back then. And it turns our that is exactly equivalent to taking the second integral of the acceleration by newton integration!! You make a small step in time dt (Which we call a frame) and you multiply by the function (speed) the add the result (Add it to the position), and you so this for a while range of time in this case And in general, thats fundamentally what video games ARE. They are a computers way of leveraging integration over small steps (called frames) to solve a potentially very complicated set of differential equations

[@sebastiangudino9377]

And of course, you render all of this with OpenGL or a similar API. Which creates a 4D space that you transform scale and distord with 4x4 matrices (called afine) and then project to 3D and subsequently to 2D using a camera matrix. Si games will also teach you a lot of Linear Algebra

[@victorinosparkajen9405]

I needed to subscribe because this series is bringing me back to high school. I took AP calc and in college in my high school senior year, then took the college placement test and was placed into calc 1. they gave me the option to instead receive 6 trig credits to satisfy my college math requirement. I did. I neglected my math for the rest of my college life because I thought "who needs math when you are going for a fine art degree?". I was so wrong back then. thank you for reigniting my curiosity of math after 20+ years. The abstract nature and creativity required for math really goes hand in hand with artistic creativity.

[@xxxSwiTcH93xxx]

Hey, I just wanted to say thanks for this video series. Awesome job!

[@zuckmansurov2781]

This is arguable the best math explanation video I have ever watched. Just insanely good explanation.

[@WildStar2002]

This series is really outstanding. Clear, interesting, accessible. Thank you so much for making these videos and for making them available to us!

[@alexsere3061]

never stop teaching math, you have a gift, I have Known calculus for over two years but this series truly made me understand so much more. Amazing Work, keep it up

[@theflaggeddragon9472]

From what I've seen, the main requests for another "Essence of" series are real analysis, complex analysis, group theory/abstract algebra, and topology. Any of these series from you Grant would be a gift from God. Thank you so much for these videos.

[@chiyanyu553]

The Flagged Dragon also probability

[@Vikas-patel31]

One of the best videos i have ever seen for integration in whole youtube. The concept clarity from fundamental is great. The whole playlist is so fucking good with top quality content.

[@AntonioMac3301]

Holy frick look at those animations at 15:42, how the rectangles shift dimensions and how the area forms a wave, so pleasing...

[@falikousoumaoro9831]

Yeah, his animations are wonderful. I just would like to know which tool did he use to make those animations?

[@isavenewspapers8890]

@@falikousoumaoro9831Manim.

[@marcus_aurelius8214]

This and the last video are godsends. I've never had a teacher explain L'Hopital's Rule and Integration so clear and concisely as he does. Thank you for everything

[@cliffordwilliams9597]

Haiku for Calculus: Unfathomable beauty in infinite curves Elusive, yet plain

[@aleksandratomic328]

I love you, Grant, I would come here completely terrified of these concepts and your voice and animations would just instantly soothe me. You're my math pacifier. Thank you.

[@chidambaranatarajan6317]

Thanks Grant for such wonderful video series. I truly started falling in love with maths again!

[@wtblessing]

I’ve been almost obsessed with these videos recently. Got imtroduced from Stand up maths (which I also thoroughly enjoy!) but these videos are just so absolutely wonderful! I can listen to them as background or as I go to sleep because the content is so smooth and calming (well-written script, calm voice, pleasant enthusiasm) all so wonderful! Or I can focus on it intently to really absorb (relearn) theses deep mathematical topics. Absolutely wonderful! I very much appreciate and take advantage of all the work that has gone into planning, preparing, and making this amazing content. Thank you so much!

[@dikshhao.o4171]

Why is this so intuitive man? I'm in grade 9 and I'm studying additional maths for my IGCSE boards. I looked everywhere for explanations of differentiation and integration and this just explained everything so intuitively. Thank you so so much ❤️😊

[@priyankaagrawal2321]

same man. But the thing is my grade 9 just starts in a few days. AD MATH IS TOO EASY FOR ME. IM also in igcse lol.

[@mattkriese7170]

About to start Calculus II and I only wish that I had stumbled through these videos in Calculus 1. These animations are so beautifully done that I recreate and screenshot these for notes. Doing this helped me finally understand related rates questions more intuitively which were my biggest struggle in Calculus I. Thank you so much. I’m pregaming and studying all that you have provided.

[@gardenmenuuu]

The most beautiful thing I have ever seen in my life and probably the best 20 minutes experience honestly in my entire life till the age of 16

[@tim40gabby25]

Do update your comment, in due course.

[@gardenmenuuu]

@@tim40gabby25😁

[@nerazzurro1234]

I don't know how did I do to survive without these videos

[@taladiv3415]

Thank you very much for the quality content and your exquisitely explained concepts using dynamic visualizations much needed for the intuitive grasp of such difficult subjects, especially as they so dryly spat at us at the university course! Keep the good work coming!

[@adjoint_functor]

This was such a surprisingly intuitive explanation for derivatives and integrals being opposites. Good job, man. Good job.

[@lucolivi]

You treat math simple, sweet and calm as math deserves to be treated. Thanks for sharing this sense with us.

[@cubesmagic720]

As a physics enthusiast and a IPho aspirant, I can understand how crucial it is for us to understand calculus and vectors and I want to thank you for the same.

[@AndyChamberlainMusic]

It feels so good to finally be able to explain WHY the anti-derivative method of calculating integrals actually works and how it's connected to the sum definition. Thank you so much 3b1b!

[@huzaifaabedeen7119]

Ol of elasticity maximum of viscosity is a good evening sir and I am in detail please give me a KZbin channel for JEE ADVANCED and the logarithm step by step solution for JEE ADVANCED and the reaction is defined as a basic physics is defined as a basic physics question and answer show please explain me this paragraph from NCERT solutions videos practice videos and more exceptions in the first equation of the day of the day of the day of the day of the year ahead I will send it is about paramagnetic molecules of viscosity of viscosity of a person in a factory 🏭🏭🏭🏭🏭🏭🏭 to be a part but a lot is a good and I will not get the same dipole by the other words the same to you and you are you can be derived by the other day and I will not get a KZbin video 1 se to a new one of my life if the unit is a supercooled liquid by the fact and a half of a lake is the most important and a little more than the other unit is the after the same to you and you can I am a Huzaifa and the reaction of a person in a factory as well and I will not get a good and a half filled by the other unit is the most important hai is a good evening and I will not get a KZbin video of Physics Wallah by step solution containing the after school and the logarithm of a lake was absent today or the same dipole by the fact which are frequently in a circle what we can I call karna to a thread such as significance and applications for a long term and a little calculus of the following is the most common and a half filled nor the parents are spending by step solution of your JEE and a little more exceptions to be like to be a good evening and the reaction of a person who reads all this time is a supercooled of a lake is equal by the other unit of the day of the day of the day of the day of the

[@AyyubxonShuxratbekov]

Until now, I did not understand the true essence of why integral of a function gives you the exact value of the area under of this function from specific point to another point. After watching this video, things start make sense. Thank you so much!

[@mitchkovacs1396]

8:40 I've never actually seen anyone use an interrobang

[@ApplepieFTW]

Mitch Kovacs they're used semi commonly in chess notation!

[@jojojorisjhjosef]

‽th

[@EebstertheGreat]

Even in chess annotation, the permutations '!?' and '?!' are usually used with slightly different meanings (with !? representing an interesting move, which is probably good but difficult to analyze, and ?! representing a dubious move, which is probably bad but difficult to refute). So the interrobang still gets stranded.

[@NonTwinBrothers]

To me they're just visually confusing as most people are not trained to read them quickly. It's a lot less confusing to type something like "!?" in my opinion.

[@NathanTAK]

How have you not seen it yet ‽ (...I just have interrobang on my keyboard. ⸘What is wrong with me‽)

[@5gallonsofwater495]

holy thank you man! i never knew i needed that "negative area" part more than i do now

[@technoultimategaming2999]

10:32 I just got it. Yes. If we derive distance we get f(x) for velocity Ds/Dt = f(v) So if we multiply f(v) • dt we get ds which is a tiny change in distance

[@marvinho7546]

this is the best teaching (explanation or proving) of integral to me at the moment, easy to understand with the idea derivative comes from!

[@ragnkja]

When you compute a definite integral - an integral between two values - the constants cancel out, so in this case we can ignore it (and could have ignored it even if we started at _t_ = 2). However, it becomes important when taking the indefinite integral, so I'm glad you mentioned it.

[@ДавидПетров-г1ф]

This video is with no doubt the most precious calculus material I could find on KZbin and amongst many books as well... I admire your work, Grant!

[@johannmeier6707]

What I missed when you explained the substraction of the upper minus the lower bound was the graphial meaning. What you actually get when inserting any(!) bound is the whole area from 0 to this point. If you want not the whole area beause the area starts right of the center, you just have to substract the area up until this point. This happens to cancel out the constant, yes, but "full area minus not wanted area = wanted area" is a more intuitive reason as to why to substract upper minus lower bound. There's nothing special about the lower bound as it also just gives the area from 0 to this point, just as the upper bound does.

[@valentinx1107]

It truly feels very like a privilege to have access to the videos you made... I am very thankful for them! Keep up the good work!

[@SharperthanA]

You should do a series on differential equations! Maybe even differential geometry if you're like trying to make our brains mushy (in a good way)

[@squibble311]

you prophet

[@aleksandrarojas433]

Thank you so much for explaining everything so clear and detailed. The graphics are amazing, representing the concepts. Makes it so much easier to form an understanding. These videos just re-taught me two semesters of long forgotten Calculus, lol. Thanks a lot for your work!

[@johnholme783]

Another clever way to obtain the total distance travelled is to multiply the average value of the velocity by the total time travelled. This still works when using curves!

[@nexninja1479]

Won't it depend on the degree of the curve?

[@johnholme783]

Nex Ninja No it doesn’t, that’s what’s so neat about it! Such an elegant solution to a apparently complex problem. First you’ve got to find your range for which you want to compute your area, then you invert that range and then multiply it by the integral of the range in question. This will give you the average value of velocity.

[@MrMineHeads.]

Yes, that is true, but to find the average value of the velocity of the function you need to integrate, so you might as well just integrate.

[@Ayoub-adventures]

Congrats, this video has made it to my playlist of best maths videos on KZbin !

[@PopCulture51]

Thank you a lot for this series, it was beautifully done and very useful. When can we expect the Essence of probability series?

[@Jazzid123]

I am so grateful for your contribution to the understanding of math! Being a math student, I am almost dependent on your clever and insightful videos. Thanks!

[@unknownnepali772]

Now look at my teachers...i think they really don't know these things and due to such teachers students don't understand maths and science...thats why students hate...thank you very much for this knowledge...i just cant memorise formulae without understanding..i just can't....thank you very much...🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻

[@jeremiechopty890]

These videos are so relaxing to watch. I could genuinely watch these like movies with my cereal in the morning and enjoy myself. The animations are always so mesmerizing. If you guys want so see some even more mesmerizing videos, watch the ones in matrix algebra.

[@hydropage2855]

Grant, you genuinely deserve the Nobel Peace Prize

[@JannisAdmek]

These videos are truly amazing, I mean it! You explain it not only in a very natural manner but beautifully and elegantly!

[@ChristopherOkhravi]

I'm only 2 minutes in and this is *very* helpful! Thank you very much for this! :)

[@ehza]

Christopher Okhravi you’re good tutor too !!

[@0213DYN]

this is one of the best mathematics video i had watched on youtube!

[@CTK8000]

Can't thank you enough for your videos. This is one of my favorite channels on youtube! :)

[@seventeeen29]

I wish I could have watched these videos at pre-calculus level. It would have solved many confusions I've had through my academic career. However watching these at a post real-analysis level has given be a refreshing level of application, going back to the grass routes of calculus. Thanks!

[@elijahbuck6499]

third time watching, good job! a 13 year old understands intergrals!

[@jijuschreest4470]

Lol you're a dumbfuck. If you don't understand calculus when you're in your mom's womb, you can't be successful in life.

[@asterixgallier8102]

@@bigfly1391 Well, I don't have enough humor then. (I deleted my previous comment now)

[@birdsculptures]

Thanks!

[@harshchikorde9495]

sir ,please make vedio on laplace transforms

[@Shenron557]

And Fourier transforms

[@iWaZziT]

coming in chapter 10, if im not mistaken

[@EebstertheGreat]

I'm pretty sure chapter 10 is just Taylor series. Getting into Laplace transforms requires quite a bit of work building up intuitions about differential equations, frequency domain analysis, and complex numbers.

[@Adam-nh2ef]

Nope, Taylor series.

[@geraldmerkowitz4360]

To me, Fourier transform have priority over Laplace transform

[@haj5776]

This has been the most enlightening math channel of all time. I hope when I have a good stream of income that I will remember to add myself to his patreon list.

[@Warwipf]

There's seriously nobody else on KZbin who even gets CLOSE to your ability to teach.

[@szyszkienty]

You're by far the best teacher I've ever seen.

[@junaid1464]

I am in love with math now. coz of u. ty

[@mustafaa.4690]

You are the best. They should announce you to every single math student in the whole world. You are making it so easy to understand!

[@red_isopat]

25 people are dirty nonstandard analyst,infinitesimal loving peasants

[@theredstonehive]

lol