What Is an Integral?
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- čas přidán 28. 08. 2024
- A Riemann sum is introduced as a way to estimate the area between a function and the x axis over an interval and then used to define a definite integral. The concept of net area is introduced, and the fundamental theorem of calculus is introduced as a way to evaluate indefinite integrals by treating integration and differentiation as inverses of each other.
Educators HATE him! Man explains half of calculus in
Funny you think this is half of calculus
Like his demeanor?... you'd really appreciate this guy, i suspicion he is the same teacher. czcams.com/video/URC125wpMS4/video.html -42419
@Z M This is why people hate learning. Shut the hell up and let people enjoy learning something.
Riemann sums/integration is one of the easier chapters in Calc AB.
I suggest you to watch the videos of basis of calculus in Don't Memorie youtube channel it explain a lot
If these integrals were explained like this to us in schools, we would have learnt mathematics as a philosophy. Excellent explanation. Thanks.
Many thanks for your comments. Very kind.
Joshi,
Actually we were explained in decent manner. But due to pressure, poverty, fights, worry about future, need to score more and more and more being not SC, we learnt, wrote and forgot.
Akshat Joshi So true! I feel like my school life was just a waste of time.😑
+tanzeela mariam same
Why wasn't this explained to you in school? This is standard way of teaching integrals found in most textbooks.
This is as clear an explanation as it gets.
Redshift Thanks!
Please google cubic Bézier curves and CAD programs.
Indeed, but I am still having headaches trying to make sense out of it...
I believe 3blue1brown's video series is even more cohesive.
J.J. Shank
I can agree. As a matter of fact, 3Blue1Brown's videos helped me understand the concept of an integral better than this one, though both have really good content.
This video is too much for CZcams. Some people teach these things $80 per hour
Believe you me, +Burak Kerten!! Those people are really STEALING the money if they charge THAT much!!!
Kerten ne demek ya kertenkelenin kısaltılmışı mı :D
Dude, who do you know who charges $80 an hour to teach this? Or ar you just making stuff up?
Then this video is worth $10.86!
we learnt integration and our teacher did not tell about this at all
I watch A LOT of math videos on youtube and this is really some of the best material I've seen.
John Nettles Thank you!
India
3blue1brown
how the hell did this guy breakdown the fundamentals of integration so elegantly,simply and beautifully ???
Brilliant. The way you approach the concepts without throwing symbols at our face but still being clear and treating the viewers as not dumb.
10/10
Getting straight to the point! I love it! Definitely need more views.
Samii G Glad you liked it.
Wow, I'm honestly blown away I've been trying to get a more satisfying understanding of integration... and this is it
This is the best, most concise explanation I’ve ever seen on integrals. Bless your soul for sharing this for free.
II'm in the 8th grade and I wanted to get a little ahead of the concepts of my classes.
This video was ideal for understanding the integrals.
What 8th grader is doing integrals on class
Guess he wants to be a mathematician@@yaboyyoob7531
This is one of the best videos explaining math I've ever seen. Please don't ever stop producing these. You're a god send.
Amazing ! So well explained that it feels like you wrote this in my brain directly without going through my eyes/ears. Thank you so much !!
Thanks. Glad you found it helpful.
Fantastic! Thanks for the comment.
this made it so clear what integrals stand for. Thank you!
Mirei a You're welcome. And thank you for the feedback.
This video was worth half of my college semester. Thank you so much for the great explanation! Please make more videos on this topic!😃
Marvellous! I've been staring at my school material for quite some time and still I can't grasp the idea of integral until I saw your video. It took me only 7 minutes and I understand much, much better. Thank you so much for your work!
Why the hell aren't there more views?
Zahi Alsalman cause 'merica
Zahi Alsalman because because everyone else is watching a video on The secrets on how to get a girl
I know right
Thanks!
Because everyone already knows this stuff.
wow, this is by far the simplest, and most clear explanation of integration and dx I've ever seen on CZcams!
good way to learn math and english: thank you so much!
Thanks for the comment, and I'm glad the video was helpful.
I love you man! great video keep going
this video has made calculus so easy, i would recommend anyone who has an issue with calculus to this video
I knew nothing about this kind of math and now I understand it, all I need now is a teacher to go over it with me
Guys this man needs more attention
Teachers have months to explain this and can't get it right, 3B1B has an amazing series about the topic, but it's still kinda long. This is the clearest explanation of calculus I've ever seen!
This video just blew me away! I've tried to grasp the concept behind integrals for 2 months, and this is the first video i came across that really cleared my mind
I skipped like 60% of my calc classes this semester and my final is on monday...Thank you so much. This channel, or at least this video, is masterfully put together and is helping my wirey nerves calm.
This 7 minute video masterfully summed up 2 hours of university lecture. Beautiful
this was explained so well oh my god, I wish my teachers were this good at explaining. Great job.
czcams.com/video/vFDMaHQ4kW8/video.html 💐.
many explanations seem better from a 2nd source mostly because you already have a foundation of the material and a second teaching seems to fill in some areas you may have been weak on or confirm existing knowledge.
People who studied this in college commonly refers to integrals like some stuff from common sense knowledge.Which is NOT. This kind of behavior is really a pain in the ass. Thanks for clearing things up!
LOL, commonly? Understatement. Its ridiculous how hard it is to find a calculus tutorial that DOESNT ASSUME YOU KNOW EVERYTHING
I mean, to a certain extent, it is. You can't expect people to dumb everything down for you, especially when math is the subject -- in which things are usually taught in a bottom-up way
Professor, you are simply awesome. I never got a session like this before. I wish you were my professor.
Just 26 letters cannot define your beautiful effort to bring this video out before us. I am sad that this video has less number of views. But I now take the charge to promote your channel.
Thank you so much for everything.
You have been doing a great job.
May the supreme lord bless you.
Also, I request you to upload your videos on Linear Algebra. We cannot visualize anything in Linear algebra.
👍👍👍👍
Your explanation is on god level, I had to watch this video twice, but only because English is not my native language, and even then I understood better here than in my school.
As someone pretty ruddy at math, I have to say this was a splendid explaination.
20 years after my math exam you came along and explained this! Finally! Thanks!
Im genuinely about to tear up because of how beautiful this is. The concept is so simple yet so genius. Math is beautiful.
I still hate tests though.
Very useful, visualizing math dinamically makes the concepts more easy to learn.
Thank you!
Im a sophmore at high school and havent learned this in school yet,its a complicated concept but this is the best youtube video I have seen explaining it by far
bruh i spend 5 weeks trying to understand what a derivative is and this man just explained an integral in 7 minutes. what am I doing with my life?
This is the best explanation I've ever seen. It is so good that I'd rather watch this video in english than come up with explanations in my own language (spanish).
Finally someone....where were you all these years... By the way you could help lot of young people out there. Do More.
I hate how following the curriculum causes me to only be able scrape by with surface level knowledge and memorized formulas. I literally did not know what a riemann sum really is or what it means, but now I do and it was all explained to me in minutes
You are awesome.
Thanks so much! Glad you found the video helpful.
This explanation is so great that even though I’m 13 I can totally understand this and apply it to other stuff
czcams.com/video/vFDMaHQ4kW8/video.html 💐.
Beautiful, I was looking for something like that and you just did it perfect. Thank you, you have excellent videos.
+Escoba Sin Gracia Thank you.
What an elegant description. This clears up some mysteries for this particular layman. Well done.
Great effort man. You helped a lot of guys on this gig but it is impermeable to my mind.
I HATE CALCULUS!
beautiful explanation. i’ve never heard of integrals before, but now i understand their concepts rather than memorizing them.
im in year 8, im actually very glad to see people understand this, for me it was getting weird at 2:53 but hes explaining very nicely, i will surely need him when im older, thank you very much:)
It makes me feel good to find this video recommended to me, my last search was drunkards dancing and big chested girls..
LOL
Same
I have solved many "exercises", but never really understood what it was all about. Now I do. Thank you.
fantastic explanation :)
I was bored of studying integrals without knowing what they used for -_- and that feels boring...now this explanation makes me think integrals are very useful in real life. Thanks !
you did a great job.... it remained a mystery so far for normal students like us... greatly simplified......
Thank you so much! I have learned how to work these problems, but the teaching presented here brings it into clear focus. I now understand what I am doing in Calculus II.
this is knowledge,such clarity and professionalism.i don't think it's possible to elaborate this subject any better .thank you and i wish the best of luck
from turkey
Feels like the information is fluently uploaded right into my brain. The pacing is amazing
He reminds me of someone giving directions to the corner store...it is so easy, all you do is...lol. Love it!
i watched more than 10 vedios on youtube about integral and this is the best i could find
I am in 3 grade in middle school and after practicing and playing around with this (obviously using this explanation), I can actually use calculus quite comfortably.
thanks man!
The method in which you explain this topic I can't ever seen before well done explanation 👍
Nice! When I read books about this subject I never understand it, but when I see this video, I know what it means. It helps a lot,
thanks for the effort! Keep up the good work mate!
wow...going to listen to this over and over...wish my mind worked like yours...what a gift!
What am i doing here ? I ended calculus years ago! Good luck fellow students god have mercy on your soul
for the first 3 or 4 seconds of the video the voice of the presentator was ho my god so boring I was about to watch an other video but I was distracted by something and did not clicked away fast enough ... now at almost the end of the vieo I feel like his voice is so calming and clear and easy to listen to that I subscribed to the channel :-)
Bro huge respect to you!
Thank you. If only my teacher had taught me like this I would've enjoyed Maths.
Oh, it's so cool explanation, very simple to understand what integrals are and how do they work under the hood. Thank you.
I studied engineering for 4 years, and only now do I fully understand what the hell I was doing. Awesome video!
Okay, but that was too big of a jump from sum of infinite rectangles beneath a curve to integrals. Why do integrals give out the area? How was it defined? Why is it the inverse of the derivative? The inverse of the function that gives out the slope, gives out the area under it. WHY?
Bryan Keller when I was in high school I was thinking exactly the same. So the answer is as follows. You define two functions, f(x) and A(x). f(x) is a curve and A(x) is the area under f(x). Then you take the derivative of F(x) using the limit definition of the derivative. The answer that comes out of that is f(x). So this means that the derivative of a function A(x), which describes the area under the curve f(x), is f(x). This implies that the opposite operation of a derivative gives the area under a curve.
Levon Sahakian your last two sentences make no sense. I think you thought about one thing and wrote another.
Bryan Keller no, it's correct as stated
Bryan Keller so to be more clear: A(x) gives the area under f(x). When you take the derivative of A(x) using the limit definition, you get f(x)
Levon Sahakian Oh, yeah it's correct. I think I just realized the connection.
Man this is just next level of godly explaination
I from Russia. It's a pity that on Russian CZcams no videos about calculus like that. I was trying to find really good video about integrals, and I find this! In spite of this is english-speaking video, with some google translator, I in 7th form understood all. Thank You very much, I already subscribed, and liked video.
P.S. Sorry for the mistakes in text
had this video existed when i was in school, it could have changed a few things for me! great video
This is marvellous since I have now understood the concept of integration
Excellent explanation. Five stars for this teacher.
Congratulations , you have a fan from Brazil !
Welcome, and thanks!
And another fan from Brazil. :)
I'm very happy to know the real meaning of "dx" by watching your explanation.
Maybe lim(Δx->0)Δx = dx
and that "dx" means very tiny amount of the "width" of the very tiny rectangle and the "height" of the rectangle is f(x).
Then small S of the rectangle becomes "S = f(x)*dx" .
I have often heard that "dx" could be treated as if "dx" is a kind of the variable value.
However I have not known the real meaning of "dx". Thank you !
MIND BLOWN! BRILLIANT VIDEO.
Mathieu Riesling Thank you!
czcams.com/video/rorqB3QQANA/video.html
i learned more from this than in my integral subject. thank you!
your captain in this ship Glad you learned something and liked it.
Brilliant! Very well made and to the point. Thank you.
this is awesome and i love how you explain exactly how to build the equation based on what you're trying to do
Integration may be interpreted as a gathering of information between limited boundary.But sometimes it may act as a squeezing as a continuity for example a point rotating in circle forming an area and then as a volume of cone.Perhaps it may evolute from single plane to three dimensional nay be multiplayer.
A differentiated stripes getting together in forming an area in between certain boundaries.In between cos value and sine value curves it oscillate between maximum and minimum value but as a phase difference may shift between zero and 1.
In piezo electric rectangle it switch over to matrices planes of parallelogram final to linearity producing electricity in piezo electric crystals for a symmetry breaking dynamics.
Sankaravelayudhan Nandakumar.
Sankaravelayudhan Nandakumar
Well if my calculus teacher would play this video to explain integrals she would have actually tought me smth :D. Thanks.
i had no idea what integral is and this video gave me information which i get instantly, thank you for great explanation!
Thank you, it is amazing for understanding the integral concept when you study it for the first time.
I've learned my pre-university maths under 8 minutes. That was awesome!
I finally found a video that explains integrals very clearly. thanks!
Each smallest rectangle area is y (height or length of rectangle) times the width, say the width is ‘(x1-x0)’ = y times (x1-x0), i.e., what is y is nothing but y = f(x) at all times, y varies based on x coordinate value. So Area of the smallest rectangle is substituting y=f(x) in the product above becomes f(x) times (x1-x0). This is proof for Area S = f(x)(x1-x0) in the 1st step. / not obvious for first timers who may assume it is so as teacher said as a statement. But simple substitution.Cheers!
I love your video! Thank you so much, I barely know how to thank you for these simple yet genious videos!
Thanks for the comment. Very kind of you.
Amazing! I've never thought integral could explained this easy! Awesome explanation!!!
An excellent tutorial/visualisation accessable anytime, anywhere by anyone allowing great new potentials.
Short and to the point only one bit of criticism, for a math novice that's curious what an integral actually is, this will appear very confusing To remedy that I'd suggest illustrating an integral as a real life object, much how the number e can be illustrated as accumulated interest from a a bank.
Great work, you explained it much better than my teacher and in less time.
It's been a while since I finished my Engineering. Nice little throwback session.
Good explanation.
I remember my Mathematics Professor talking about graphing lines in College Algebra and all of a sudden stopped and asked "is it possible to find the area of this function?" We were all dumbfounded and answered no as Algebra students at my university probably only did some geometry prior to the class and thought this squiggly line is not a shape, therefore not containing a formula to use to solve.
Here I am a year later showing people how to calculate the area using integrals.
Going through calc 2 was such a dread because it was like drinking out of a fire hydrant. When you actually take time and look over this stuff again its quite fascinating
This is really-really good. I think my teacher didn't really understand the underlying concept of an integral or maybe he didn't really know how to teach in an easy way.
Best explanation I've seen so far in a video. Salute!
I am a 6th grader, and I can even understand this video because of super good explanation
Tie the differential to the integral-s (not after the integrand!) and make the "d" upright to have a proper expression-style for an integral: $\int \mathrm{d} x$ e.g. Yet a neat way to show how Riemann Integrals work. Lebesgue is superiour in terms of math-proofs, but won't differe in terms of the solution.
This is the best video i have ever watched on youtube
Even if it's an infinitely close estimate, it's still an estimate. Calculus seems to be a way to work around not understanding the area inside of irregular shapes instead of a way to really understand them. This seems basically to be a way of writing an infinite number of infinitely small widths multiplied by an infinite number of infinitely small heights.
Thank you for covering the very basic definition of integral! I really enjoyed this video!
You need more views. This is a great explanation.
Much much better than Khan Academy
Thanks! That was one of the goals.
Maharshi Chakravortee Savage !!
Thought exactly the same
Soo true