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Definite integrals intro | Accumulation and Riemann sums | AP Calculus AB | Khan Academy

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Introducing definite integrals, which represent the net area under a curve. Learn what this exactly means and about the notation we use to write them. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-accumulation-riemann-sums/ab-def-integral/e/understanding-the-fundamental-theorem-of-calculus?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-accumulation-riemann-sums/ab-def-integral/v/evaluating-definite-integral-from-graph?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-accumulation-riemann-sums/ab-def-integral/v/introduction-to-integral-calculus?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago. About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1 Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
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Text Comments (15)
Jake Sykora (9 months ago)
Hello calc class
Daniel Smadja (10 months ago)
What is dx?
Renato Lopez (9 months ago)
its just the length of each square inside the integral. It gets closer to zero as the squares get smaller because they decrease in length and also more are added to the total integral area.
A. Vahidy (9 months ago)
Yoni Smadja dx is the difference between two points . A difference which is almost equal to zero , but not zero . U might say this difference is equal to 1/100 or 1/1000 or 1/100000000 or 1/10000000000 , yes the amount of difference which I mentioned above is very very small and almost equal to zero , but they are still some values which you can see and count. dx is some thing that small that a human can't imagine . It's just a previous point before zero , which is obviously not understandable for humans.you can make any number as small as you can by putting more zeros in ur denominator as I did in above examples, but u can never achieve to a point which is just a previous point before zero. So the conclusion of my comment is that dx which is a difference between two points Let's say difference between points X and a so , dx = x - a Such that x is almost equal to a Which we say in mathematics as" x proceeds to a" . An arrow symbol is used to say this phrase which I don't have here. Than you can say that dx proceeds to zero It's a very beautiful concept in mathematics derived by humans. As we are staying at a same point because x and a are almost equal but at the same time we find a difference at that point. Hope.u get something..
critic7337 (10 months ago)
New drawing tool is slick as hell, Sal!
Nick W (10 months ago)
Wow he's really mastered the art of drawing a straight line :P
Ishan Dangi (5 months ago)
Nick W he used the shift key
Linus Torvalds (1 year ago)
Very helpful video, please keep doing videos about mathematical theory
Which software you are using ........and hardware.....please tell Khan Sir if possible?
Hypnotica (1 year ago)
I cannot put in words how helpful this approach of really understanding the theory behind the mathematics is, rather than just memorizing things like the Õ great educational system tells us to do.
Hypnotica (1 year ago)
PS: After you're done with Differential Calculus, It would be really great if you do the same approach of explaining the theory behind Linear/Multi-linear/Matricial and/or Tensor Algebra. Or maybe get into Stochastic Calculus as it's on the same lines of the current series. Applying your approach to these subjects would be really enlightening since they almost look daunting when you try to get to the bottom of the theory.
Heavenclone (1 year ago)
That is definitely an integral.
Vtron (1 year ago)
Thanks for Doing these videos again better
Aniket Sharma (1 year ago)
Please can you decrease the size of the cursor, as it distracts and doesn't let concentrate on what you write.
Abhiram Upadhye (1 year ago)
First to comment. Once more a very helpful video. Thanks Sal Khan, keep your good work going

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