Riemann approximation introduction | Accumulation and Riemann sums | AP Calculus AB | Khan Academy
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- เผยแพร่เมื่อ 5 ต.ค. 2024
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Approximating the area under a curve using some rectangles. This is called a "Riemann sum". Created by Sal Khan.
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thanks Sal, I'm watching this in 2024. You're the GOAT.
i like how you said have fun
I m actually having lots of fun learning this, whereas during class I couldnt follow the teacher fast pacing.
Which is why learning theory via videos is the future IMO.
Playcool18 Most of the teacher do not take time learning how to make lecture understandable or interesting, they just focus on the knowledge and “quiz and test”,this is why lost of lectures in schools are dreadful
Think you meant to say "1.5" instead of "1.25" at 4:31. I don't care though, I still love you. You're always there when my textbook fails me. :)
you know, on the khan academy website, they showed that he made that mistake.....so yeah!!
6:10 I don't wanna give up any of that "pink area" Sal..
Great lesson, as always.
the best way to introduce the work
this helped me so much thanks !!!! so useful
can't wait for next lessons!
So much more clearer now.
THANK YOU
thank you sir............
Concepts are much clear now 😌😌😌
really cool!!!
would it be more effective to take out delta x as a common factor once all the multiplications are laid out?
Why did you say 1.25 and 3.25 instead of 1.5 and 3.5.
I'm gonna assume it was a mistake but just making sure there is no real reason.
Well what is 1.5^2+1? He is right.
He’s khan
why dont you just take delta x out to the front and put the rest of the function sums in the bracket
He effectively did that in the final step. The purpose of leaving them in is to illustrate how each delta-x functions as one of the terms for computing the area of the rectangle.
Why is it 4 rectangles?? When you subtract a and b do you always divide it by 4?
No, you can take as many rectangles as you want.
how would I calculate the overestimate with this same exact example?
President Donald J. Trump... at each delta x you form a rectangle and make it to where the rectangle's top right vertex is on the function. On that point is where you evaluate f(x).
Lee Hernandez thank you very much!
MQ 786 progress
Is the exact area under curve [1,3] = 9 2/3?
the king
Do we not need to add on f(3) x 0.5
Or is it not in the equation??
No because you're evaluating at the first endpoint so you don't include f(3).
Do you always want to have 4 rectangles to evaluate
No you will be given an interval where you can find deltax and see how many rectangle you have
Also (but this is probably way too late) the more triangles that you draw the better the approximate for the area is
Here you will need to use rectangles not triangles, but yes the more you have.. the better that is why we use the limit as the number of rectangle gets to infinity.
Is this method ever used again in Calc 2? It's not difficult to understand, it's just intensely tedious, esp after learning integration. Are there any instances in which integration techniques cannot be applied, and Riemann approximation has to be relied on?
His Voice is so relaxing
Why 4 as the width?
4 is the number of rectangles
These look like Darboux sums :o
Alvin the Chipmunk Whats that?
Quarentena
Pls make the screen white
How can u take the exactly 4 rectangles ?
take the difference of a to b then divide by 4. After, add that to your a untill you get to b
can u work on not repeating the same 2 words so many times while you're writing something, its kinda annoying
+ajferrer96 Honestly stop being so picky. So many people have found this useful. He's doing it so it solidifies in your head.
He's a verbal processor. Back off.
wrong explanation
Study With You ...congratulations?