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Introduction to integral calculus | Accumulation and Riemann sums | AP Calculus AB | Khan Academy

1027 ratings | 176411 views
The basic idea of Integral calculus is finding the area under a curve. To find it exactly, we can divide the area into infinite rectangles of infinitely small width and sum their areasÑcalculus is great for working with infinite things! This idea is actually quite rich, and it's also tightly related to Differential calculus, as you will see in the upcoming videos. Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-accumulation-riemann-sums/ab-def-integral/v/definite-integrals-intro?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-motion-diff/v/rectilinear-motion-example-maximum-acceleration?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 (49)
Ali baba (20 days ago)
why you want to know the area under the curve? that is the main question for me
Andrea Arbizu (21 days ago)
Love you
Angel xd (1 month ago)
No se supone que los rectángulos llegan tocado la función justamente en el punto medio del ancho de cada triángulo y así vez dejando un área libre y otra dentro para dar lugar a una compensación de área?
Laith Mohajer (1 month ago)
Thanks mr Khan
Trollin Charlie (2 months ago)
isthis where prople earn degrees from khan acaddmy
StephaneGrappelli (4 months ago)
Best calculus lesson ever!
snorgisborg2 (4 months ago)
I'm scared
Bala Dakshayani (4 months ago)
thank you sir i can't understand the other videos your vedio is nice
Durga Devi (4 months ago)
wow thankyou
Random Immigrant (6 months ago)
Khan Academy videos + Paul's online notes (Paul Dawkins I think) are a killer combination when learning maths/calculus. I went from a 51% (50% is pass at my university) for first year maths to 89% in 3rd year advanced calculus. I strongly recommend maths students to use these as learning supplements.
Bhai Bhai (2 months ago)
Bhai Bhai (2 months ago)
Random Immigrant (4 months ago)
+Praveen Kumar hi, If you're talking about Paul's online notes, it's not a channel, it's a website with high quality PDF's that explain concepts in detail and full examples.
Praveen Kumar (4 months ago)
Random Immigrant what Is the 2nd channels exact name and does he summarise the important points of the chapter as his name suggests.
ZombieGaming Tv (8 months ago)
What is that E like thing pls tell me pls
Dre Springfield (3 months ago)
It's called Sigma. Khan Academy has more videos over Sums & Series to help.
Gt Cline (6 months ago)
Check out this link: http://www.columbia.edu/itc/sipa/math/summation.html
John Tom (8 months ago)
Calc 2? Welcome to hell.
4am Curiosity (8 months ago)
Just wanna say i never comment on these things but thank you especially for being the best most fluent youtube tutor page online. So helpfull. The background,color scheme, explanation all is on point
AKK AION (10 months ago)
this is amazing. you have just saved me days to understand what an integral is. Thanks a lot and may god bless you
Xau Xius (10 months ago)
am i the only one hearing his voice cracks from normal to sexy? sometimes he talks normally and randomly inserts words with sexy voice
tc41986 (11 months ago)
college algebra with trig is the furthest i want to go
ummul salmah (1 year ago)
Basically integrals is just better approximation of an area beneath a curve
Luke Kennedy (1 year ago)
3:30-3:40 sounds so trippy😂
420 MLG (1 year ago)
gotta love integral calculus :P thanks for the video
Govindan Rajagopalan (1 year ago)
do not get it
unite perry (11 months ago)
first start with limits and derivative
Reinaldo IV Leon (1 year ago)
hi where can someone point me to learning trigonometry
Erick Joshua Nebreja (1 year ago)
Tried to skip from mathematical induction to integral calculus just to see how far math has become. What on earth is happening here....
John Landon Miller (21 days ago)
Erick Joshua Nebreja that's the base principle
John Landon Miller (21 days ago)
Erick Joshua Nebreja basically we are looking for the area under the graph. For small changes in x, we multiply it by y (area of a rectangle) to give us the approximate area under the graph in between the x values we chose.👍
TOXIC (6 months ago)
Same LOL
Trever M (1 year ago)
Is this real? I feel like you people write these strange and random letters to make us dumb people look even dumber. This is all craziness to me.
Penguinox (1 year ago)
Calculus and math is a ladder to be conquered. It's basically like learning the language of logic. You're not dumb for not understanding it. It can make sense to any dumb person if they learn it from the ground up. There ain't no shortcuts.
Anuj Arya (1 year ago)
Watch my video gyz
dodiloi (1 year ago)
I have a Déjà vu
Nalini Awasthi (4 months ago)
Vy The Fujoshi (1 year ago)
Bless Khan Academy
Vikram Singh (1 year ago)
Hey everybody can someone point me to where I can start learning calculus 1? Would that be limits?
elplebe12121 (8 months ago)
that is correct, just make sure your alg and trig are good
Vikram Singh (1 year ago)
+Ardian thanks man, I'll keep all that info in mind, appreciate it!
Vikram Singh (1 year ago)
+ADHD God thanks man, is there anything else in calculus 1 I should study as well?
brownpolyestershirt (1 year ago)
Found this channel on through my current professor. You explain things better than most math profs I've ever had. Thanks so much for helping me meet my goals.
L borate (1 year ago)
I love khan academy!! 3blue 1 brown has a great playlist on integrals also!
T.T. O.T (1 year ago)
What kind of drawing tablet do you Sal use for the videos? Is it a cintiq?
Anuj Arya (1 year ago)
Hey art lovers watch my drawing video
Urmila Kumari (1 year ago)
thank you Sir.
paige collyns (1 year ago)
Hi I watch you in class
First thanks

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