Area between a curve and the x-axis | AP Calculus AB | Khan Academy

Based on the fundamental theorem of calculus, we can use antiderivatives to compute integrals. Created by Sal Khan.

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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[Triyoger]

Almost 11 years and you’re still helping students out 💯

[Seafaringslinky]

I've just got to say that you all are the biggest help in the whole world, thanks so much!

[sprmario]

why is this 5 minute video more informative than my two hour calc class?

[ozzlicious]

Everyone watch at 1.25x the speed. It is much faster and equally understandable. Good luck and God bless :D

[Dhanyerese]

Within 5 minutes, it became so clear! Thanks!

[ilikebacon]

that just alleviated my fear of definite integrals. I thought I had to evaluate it and get the sum of all values between the two numbers.

[vishalbhatia]

The sign for Integration comes from the LATIN LONG 'S' which essentially is short for Summa which in turn is short for SUMMATION which is what Integral Calculus is all about.

Leibnitz was the first person to use that symbol!!

The letters dx stand for INFINITESIMALLY SMALL particles of the variable x in this case

Hope this helps.

[spankymebottom]

ty. the integral videos are superb and I'm having an easier time with this than limits themselves. is this usually the case for most people?

[bayekofsiwa]

Made me learn it for about OMG Commended Khan Academy!

[fergiefergie]

Slowing it down to .5 makes him sound drunk. lmao

[HenggaoCai]

You should post more practice problems online. Post some Optimization and related rates problems that are three times harder than the AP exam.

[Kino-Imsureq]

its cool that when you have f1(x)=ax/|x| and you have variable A for an equation, the y axes will be flipped where y : 1 => y : -1 and y : -1 => y : 1 *IF* the point is below x : 0

Is there anything that I can do to help speed up the development of those integration practice exercises?

[FrankEgan]

Can you do a video on proving the area of a circle using integrals?

[richardmaurice]

Here to study for a calc final tomorrow, anyone else?

[Kino-Imsureq]

tried the equation on desmos it worked :)

[TheALevelStudent]

When do you plug in functions then? Isn't that definite integration?

[salsenani]

Khan: 0:1 *&^%^&*&^^%^&*(*&^% 5:37
me: ammmm !!!????
khan : 5:38 sixty three over three, and three goes into sixty three exactly 21
me : finally some thing i know

[recursor]

Wait what about the plus c's? Is it acceptable to discard them and not even write them out in this situation?

[vtron]

My video about definite Integrals is exactly like this but with real paper