Introduction to integral calculus | Accumulation and Riemann sums | AP Calculus AB | Khan Academy
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- Опубликовано: 21 авг 2024
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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.
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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.
Random Immigrant what Is the 2nd channels exact name and does he summarise the important points of the chapter as his name suggests.
@@PraveenKumar-kh5ns 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.
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Thanks for the tip !
I was very bad student in first school, almost completelly absent in high school. After more than 20 years at the age of 42 I have started to study Computing, thanks to Sal I achieved distinction in math 100%, while having undiagnosed strong adhd- inattention. Khan Academy is the future of learning. Thank you Sal and other people that helping people to educate themselfs. P.S. Sorry for my grammar if it is bad, I never took english class.
Thats great! Im happy for you 😁👍🏻
I just started a bachelor degree in industrial engineering. Heavy on math. Never had that kind of math In my previous school. At 47 let’s see how far I can push my knowledge
I always get chills when I listen to Mr.Sal explaining the subject. He really takes you through a journey where you not only learn how to do the calculations, but also _understand_ the wonder of our complex & interrelated world. It's truly awe-inspiring. Thank you very much Mr.Sal
Told me EXACTLY what I needed to know. As opposed to any other source I could find. Thank you so much!
Tried to skip from mathematical induction to integral calculus just to see how far math has become. What on earth is happening here....
xD in our school this is what some freshman in high school are learning
Go take a peak at topology or tensor calculus ;)
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.
Yall explain things better in a shorter period of time than all of my previous teachers most brilliant moments combined.
I love khan academy!! 3blue 1 brown has a great playlist on integrals also!
It's "too" not "also".😉
Learned how to count to 4 when I was two years old. Been earning a tremendous income as a professional musician for the past 45 years. Every once in awhile, I play a waltz...in which case, I only have to count to 3. 😁
keksksksk
lol
Nice comment, but why in this video?
@@coolteateacool905 😐 Uh, because I have no friggin’ clue what he’s talking about. I was just being funny.
I apsolutely love you guys, went from medical high school to engineering college with little knowledge of calculus. You helped me with both integrals and derivatives so thank you ! Hope I pass my Math course ! :D
absolutely
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
6 years later and this is still godly. You rock brother
I escaped high school without any exposure to calculus and, as an English major in college, escaped it again. But my curiosity never ceased . . . now I can learn without the pressure of a grade!
been with khan academy since algebra 1
why am i paying so much when youtube can explain what my prof did in 30 mins in 4 mins
because how are private corporations going benefit off you otherwise?
Because you are paying for the diploma not for the education
They know the paper is so important to your ability to earn money, so they gouge you accordingly, but since they're semi public and are subject to state auditing, they hire their buddies as "chancellor's of diversity" or something like that to justify tuition increases.
For the certificate
gotta love integral calculus :P thanks for the video
Thank you! Very easy to understand, now I also know about integrals! Thank you very much, hope you enjoy your day!
im in yr 8 and i learnt integral calculus from this guy
this is amazing. you have just saved me days to understand what an integral is. Thanks a lot and may god bless you
so apparently I need integral calculus for my Physics IA (IB kids you know what's up) so now I'm trying to learn all this 6 days before the IA is due
college algebra with trig is the furthest i want to go
Thanks to video like this, I have a better understanding of math
Hi I watch you in class
Bless Khan Academy
3:30-3:40 sounds so trippy😂
Luke Kennedy lmao what?! 🤣
def my favorite part and the only thing I understood throughout this whole video
What kind of drawing tablet do you Sal use for the videos? Is it a cintiq?
do you know wish software he uses ?
You are the Grand Saviour My Friend
May God give
like , what could you possibly need
More knowledge
MORE
I think I’m getting ahead of myself in trying to understand this.
if you get derivatives first, then it becomes something beautiful I say
This was AWESOME!!!
Thanks mr Khan
Thanks for helping me teach caculus
wow thankyou
thank you sir i can't understand the other videos
your vedio is nice
Youre explain is very good. i forgat what mean the integral calculus and when use it. but now i can remember
Teacher!,your video is amazing I love this subject and I will teach my student follow from you
Thanks teacher for teaching video!
thy is the maths god
So happy for your video explaination 😍😍😍
THank you
u r the best teacher ...chemistry, math etc
yes!!!
"Our journey of integral calculus" has been non-sensical so far
Thank You Very Much ...
Please help the Khan academy app isn't working!!!
Edit: its working now thanks
Why would you want to find the area under the curve? Is it just to calculate volume of real world things, or is it related to the graph?
thank you Sir.
Calculus is just a mathematician that looked at literature and said, “I could do that.”
Integration is much more than finding areas.
Basically its about finding the WHOLE (W) given the fancy name Integral (I) from its Individual (not average) components (ICs) given the fancy name the "derivative". So finding the W fom its ICs is the same as finding the Integral (I) from its derivative.
Now if the ICs or derivatives are mini lines the W or I will be the entire length as in finding the Length of a Curve. If the ICs or derivatives are mini areas the W or I will be the Whole area (under the curve). If the ICs or derivatives are mini volumes then the W or I will be the whole volume. If the ICs are mini Forces the the W or I will be the Whole Force and so on. Nothing special about AREAS at all.
Clear explanation
Thank you, but what's the answer?
My boss just wants the number and unit of measure. 28m²?
amazing thank you
I love 3b1b, but his videos on what an integral is come off as very convoluted to me; this ~5 minute explanation is much more clear. Thank you
the word you most used is infinistesinefily small
Thank you
Incredible
This sound behind the videos, thanks a ton, you have taught very most concepts in fundamentals of mathematics best in the world.
In autocad i would just draw any wonky curve and it would automatically know the area.
the real question is would it you help in examns
This have at you.!!
Ahhhhh thank you sm ily bye
Hey everybody can someone point me to where I can start learning calculus 1? Would that be limits?
+ADHD God thanks man, is there anything else in calculus 1 I should study as well?
+Ardian thanks man, I'll keep all that info in mind, appreciate it!
This is so f*cking cool.
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?
First thanks
Could you please tell me how to know that integral of 1over x is ln x ... how they could know this in the first time ... what did they use series .. limits ..?!
Is there any example how to exctract the rules from its origin not only to memorise them
Love you
isthis where prople earn degrees from khan acaddmy
Basically integrals is just better approximation of an area beneath a curve
NO! It's not quite a "better approximation"...it's suppose to be the "exact" or analytical area beneath the curve. It's the same as the derivative which gets the "instantaneous speed" rather than getting a good approximation. That's the power of calculus! By using the concept of limits, we can get the exact area or exact slope of any curve.
@@felixchien1664 no not exactly. Limits are mere boundaries that a certain continuous function will keep on approaching, but will never arrive at. It will just keep on approaching infinitely. So there's no such thing as 'exact' area under a curve or an 'instantaneous' rate of change. We'll never get exact and instanteneous values using limits knowing its inherent numeric limitation.
@@No_BS_policy hmm, not sure if I agree actually. The concept of limits is that there is a definite number as something approaches a number (or concept like infinity). You shouldn't look at the limit of "n approaches infinity" as a "limitation" or "approximation". For example, the "limit of 1/n as n approaches infinity" is precisely 0. It's not that it approaches 0; it IS zero. A limit is a number. "It is not a process, nor an approximation, nor in any way imprecise."
The law says make me look like a joke and I'll leave ya feeling like a fool
What is that E like thing pls tell me pls
Check out this link: www.columbia.edu/itc/sipa/math/summation.html
It's called Sigma. Khan Academy has more videos over Sums & Series to help.
I have a Déjà vu
Physics
ive just been this place before! HIGHER ON THE STREET
Deu saudades de meu tempo de faculdade.
Why is a down there and b up there? What is dx? What's going on?? :(
Before starting integration you should go through the derivatives first they're connected you'll understand what dx is once you learn the derivatives
I'm scared
Isn't it crazy who two opposite forces; that n gets infinitely large and I gets infinitely large have a symbiotic relationship? Litterally a paradox gives the most accurate summation you can never reach 😂
I'm incredibly grateful for Kahn Academy. I'm studying math in my free time before I pay for math courses. I love how simple they break down complicated ideas like integration. Derivates are neat and intuitive. Now integrals are short-of intuitive but to abstract still
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.
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.
Lol I fought the law once and the law won
Any1 here after new vsauce video??
💙
G...
💙❤
Indian kids learning this at 8th grade
*doing shhhh sign*
❤♥️
🗿notation
do not get it
first start with limits and derivative
So now tell me, WHAT IS THE INTERGAL OF X!
Can someone explain what do a and b define? are they like i and n?
a and b are the lower and upper bounds respectively of the entire region you’re trying to find the area of on the x axis, they have nothing to do with i and n.
n refers to the nth piece that you want to find the area of, and i is just used in the summation to make it clear what exactly you’re doing
^(If you need a better explanation of what i is in this case lmk because that explanation admittedly isn’t very clear)
Bruh what?
im 10.
I have no idea what this is but idc
God will help you. Get supernatural help. God is always on your team. God wants to be a part of your day. God wants to be a part of your schedule. Make room to spend time with Jesus.
am i the only one hearing his voice cracks from normal to sexy? sometimes he talks normally and randomly inserts words with sexy voice
This is all u notice after the introduction to Calculas?
Sal khan deep voice