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

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.

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.

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[CStrikr]

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.

[flowingmind]

Is it only me or the video cuts off abruptly at 2:27, I'm frustrated that I can't watch it till the end

[nickw]

Wow he's really mastered the art of drawing a straight line :P

[cariboux]

What is going on with this video... It says 7 minutes but cuts off at 2? It does the same thing on the app. It cuts off in the middle of him talking.

[nicholasv]

You draw perfect straight lines!!! OMG

[qualquan]

Integration is NOT just about finding the AREA but about finding any WHOLE (W) called the Integral (I) given the Individual Components (ICs) called derivatives of that W or I. In brief it's about Individual components (ICs) called derivatives and the WHOLE (W) called the Integral (I) of the given ICs or derivatives
Thus if the ICs are individual mini lines, then the W or Integral is the length of the Curve. If the ICs are mini areas the W or I is the Whole Area under the curve. If the ICs are mini volumes then the W or I is the Whole Volume. If the ICs are mini ANYTHING like Charge or Force or Energy etc. then the W or I is the Whole Charge or Force or Energy etc

[vtron]

Thanks for Doing these videos again better

[critic]

New drawing tool is slick as hell, Sal!

[aniketsharma]

Please can you decrease the size of the cursor, as it distracts and doesn't let concentrate on what you write.

[linustorvalds]

Very helpful video, please keep doing videos about mathematical theory

[vhapniphysics]

Which software you are using tell Khan Sir if possible?

[abhiramupadhye]

First to comment. Once more a very helpful video. Thanks Sal Khan, keep your good work going

[antwanwimberly]

What’s the point of dx??? It seems like it just gets ignored most the time!

[supernaturalstrength]

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