If you want a bit more detail I'll give it to you. The common way to do integrals is the Cauchy-Riem man integrals, which is this definition. Imagine you want the area under the curve between a and b, then split it into an n amount of strips.. So let's say you do 3 strips your interval looks like a - c - d - b. Where every - is a strip Now for every strip you can take the value before it, plug it into the function to get the height, and calculate the little rectangle (Now, the Cauchy-Riemman integral actually says that, no matter which point you take along the strip, the definition works, but that's a bit too complicated) This gives us the rectangles.. BUT we can clearly see the area is either too much or too low (like in the video).. to get closer to the stra we can set n = 100 instead of 3 right? And what about 1000? Since you're summing the little rectangles, you call that a Cauchy-Riemman sum, and as you take the limit as n approaches infinity, the approximation is closer and closer and closer... Until it's eventually (at infinity) exact This however doesn't explain all integrations, it works for most but there are other definitions of the limit... The fun thing is they all give the same result tho!!
Yoo ai has blown up out of proportion. It’s still a shame that there are so many laws making the exploration into furthering the human IQ illegal. We could’ve solved violence, discrimination and war but instead we had to make certain experiments and practices that would boost IQ illegal. WTF world! Oh wait, it keeps those at the top secured knowing we are all kept stupid by the system, now it makes sense.
@@iamnoob3931 yea, because I straight up didn't, my teachers are horrible and don't know how to explain anything correctly, they shouldn't even be teachers
No way... no frickin way... I understand it now, thanks short creator, I'm actually mind blowned right now. Edit: Damn... some people be saying in the comments "you SHoULd be uNDerrStandINg this ItS BaSIc?" For the record I understood it the moment I learned it (I have one of the highest grades in my calculus class), just not as fundamental as this, as to WHY it results in this as opposed to just remembering formulas then regurgitating it at a test. Now move along smarty pants, we get it, your oh so smart 🤓. Want a medal? Lol.
This is the most intuitive description of integration that I have ever heard. That question “sum of what??” points out what really matters. Real example of asking good question.
unironically, this actually made integrals make more sense, no other tutorial i saw actaully said that dx is the width, it may seem primitive, but it actually took me some time to understand
To anyone learning integration from this video: As you make each strip or dx smaller, the approximation of the area under the curve is better. Doing the calculation using integration techniques will provide infinitely small strips (dx) and will give you not an approximation but rather the perfect answer
Seen 5 or something of your videos. This is what content creation is all about. New things in the saturated platform. Learning with fun. Education niche never ever will get old unless it's some boring old ass classes. Keep rocking bro 🔥❤️
So basically, what you do is do the opposite of a derivate ( i don’t know it’s name in English) So X^2 becomes 1/3 X^3 Then you put it inside brackets and add the 0 and 0,5 just like in the vid but with the brackets : [1/3 X^3] from 0 to 0,5 (i can’t make them little to the sides but it just like the video) Then you replace X with the bigger number (in this case 0,5), and you replace again with the other number (0) And you subtract the one with the small number from the one with the big number So it will be : (1/3 0,5^3 ) - (0) And ≈ 0,04 mu or i don’t remember the unit And to convert it to centimetre square, what you do is 0,04 x ||j|| x ||i|| (Only those who knows will understand i don’t remember everything sorry y’all I’m bad at explaining too)
so you add one to the power so x^2 becomes x^3 then divide by new power so x^3 becomes x^3 /3 now youve integrated it, you want to find the area under the graph between 0.5 and 0 on the x axis so it's (0.5)^3 /3 - (0)^3 /3 which equals 1/24 and that's the area under the graph between those two x coordinates
Well that's more like memorization by you. Like adding one power and dividing by the new one. Kinda weird 😂 Do you know why the change in the indefinite of the function(here x² for eg) from the upper limit to the lower limit gives area? That's the 2nd fundamental theorem of calculus and one thing everyone MUST know why but nobody knows it just hate on this great topic
This person memorized rules. Exactly what you should do when learning maths. Good luck doing any type of maths without them. Unless your name is Isaac Newton of course.
From what i've learned, the "s" symbol he states is the symbol for the operation of antiderivative, as in taking the anti derivative of something, atleast from our teachers explaination. Though it being sum is a way nicer way of remembering what to do with it. Another note: doing this will not give the exact area under a curve but rather an approximation of it.
The s together with the dx is the simbol of the anti-derivative. But if you don't know the idea behind the notation, it will seem quite mysterious and arbitrary. Also you're leaving a lot of intuition on the table. This sort of pedantry from mathematicians is part of the reason why people find math difficult. They take a simple concept and explain in a way that is perfectly logical and formal but completely unintuitive. The thing is, the people who came up with calculus started from the intuition and then the formalism was developed over the following decades. And yet we teach it backwards. The same problem happens with teaching language; you get taught the grammar first, even though that's not how native speakers learn their language.
@@jessetallman2142 I may have learned calculus but do I know how to apply most of it to real world scenarios? Yeah that's a no, I really don't know what it would be used for atleast for the common public, but im sure there's a use for it somewhere out there.
@@amountedak9246 obviously the schooling didn’t affect your intellect. That wasn’t the question id you dont know what a stem field is i doubt youve stepped foot on a uni campus.
@@jessetallman2142 Maybe I just misunderstood the question though I do know what a stem field means, but you would still be right about me not having been to uni as that is just a plan for now. Field wise, i'm not really sure where it would be needed either as I haven't really done much research into what i'll be taking in the moment
I fucking crying while reading intergration for hour!!! But now after the f exam... this vid pop up in the middle fuckin 3:20 AM?!! Man why ;-;(yea i failing my additional math exam like fr)
You could also use the trapezium rule, which is way longer but it’s still the same result(trapezium. Rule is an approximate though so it usually is a bit less than actual integration with limits). Furthermore, for trapezium rule you need to table out your x and y values and find distance between. Trapez. Rule = 1/2 x width (y1 + y last + 2(y2+y3+…+(ylast-1))
Not quite as you will learn in advanced differential equations but I really like this explanation to learn about how to do integrations of functions without complex terms like imaginary numbers. I haven't really got it yet so I can't explain very well. 😅
Not really though.. it’s not the average but rather taking smaller parts (or rectangles) and adding them up to find the sum of all parts or in this case to find the approximation of the area under the curve between these given values and this given function. That’s why it’s also known as the Riemann sum. But hey I could be wrong too. 😅
It’s actually the limit as n goes to infinity of the sum. This allows those boxes on the screen to be as close to the actual function line as possible. 👍🏼
@@yuvalkoren4070 oh. Either way you mean that, i agree I got the formula from desmos. I perfected it until the numbers were right It is x^z+1 - y^z+1 /z+1 Where z= amount of x in the int So using this, int(2,1,1)=1.5
@@mihaleben6051 a bit complicating stuff, it's quite standard, highschool level at most. The integral itself is x^3/3 and then the final solution is (0.5)^3/3=0.125/3
We have ai goggins explaining math before gta 6
It ain't real it real I was edging
This shit is a fever dream
thats not ai
I love how goggins not only teaches it how to caluse our minds, but also math😊
Fr bro 🔥🔥
BROOOOOO !!!! The "sum of what" is my question since I have learnt the existence of integration. THanks for the explanation. Massive thanks.
If you want a bit more detail I'll give it to you. The common way to do integrals is the Cauchy-Riem man integrals, which is this definition. Imagine you want the area under the curve between a and b, then split it into an n amount of strips..
So let's say you do 3 strips your interval looks like
a - c - d - b. Where every - is a strip
Now for every strip you can take the value before it, plug it into the function to get the height, and calculate the little rectangle
(Now, the Cauchy-Riemman integral actually says that, no matter which point you take along the strip, the definition works, but that's a bit too complicated)
This gives us the rectangles.. BUT we can clearly see the area is either too much or too low (like in the video).. to get closer to the stra we can set n = 100 instead of 3 right? And what about 1000?
Since you're summing the little rectangles, you call that a Cauchy-Riemman sum, and as you take the limit as n approaches infinity, the approximation is closer and closer and closer... Until it's eventually (at infinity) exact
This however doesn't explain all integrations, it works for most but there are other definitions of the limit... The fun thing is they all give the same result tho!!
@@zerokun2655Hey thanks for talking out your time to write this comment, I truly appreciate it 😁
@@tlpthelowlevelpros5909 no problem man! I loved studying this in University and love to share
this isnt a good explanation either, watch the video from 3blue1brown for a good explanation
selling our secrets. watch 3blue1brown hes where i learned it from
Task - Write an essay on dangers of AI
Me - Have you seen goggins teaching maths
Technically if we get the human level intelligence we're cooked
@@Trinity_editz0yeah can’t wait to not have a job and be poor for the rest of my life
@@zippyflamez4597I already am
@zippyflamez4597 majority of the populace is. Middle class is a small portion and the rich is an even smaller portion
Yoo ai has blown up out of proportion. It’s still a shame that there are so many laws making the exploration into furthering the human IQ illegal. We could’ve solved violence, discrimination and war but instead we had to make certain experiments and practices that would boost IQ illegal. WTF world! Oh wait, it keeps those at the top secured knowing we are all kept stupid by the system, now it makes sense.
This literally explained integration better than I ever learned it in calculus, thank you lol
That should equate to that you have learned nothing in calculus. At least in integration.
@@iamnoob3931we learnt formulae
@@iamnoob3931 yea, because I straight up didn't, my teachers are horrible and don't know how to explain anything correctly, they shouldn't even be teachers
I understood it and I’m in 7th grade
In all the calculus books that's literally how it is explained... With the same drawings and the same example... Always with x²... 😂
Googins when he's done carrying the boats and the logs
I hope "carrying the logs" was an intended pun
Then he’ll carry us
Bro is carrying the Logs and exponentials🗿🗿
Goggins next second after H*ll week:
Carrying the floats and the logarithms
"Patience motherf*cker" 😂😂
😂😂
😂😂
😂
😂
😂😂😂😂
Goggins: "Graph it out man"
💀💀💀
earlier - "frag it out"
now - "graph it out"
its scary how AI able to detect this kind of phrase out of goggins
As a mathematician and educator, this is the best and most succinct explanation for integration I've ever seen. Well done!
This is the clearest explanation of an integral I have ever heard
No way... no frickin way... I understand it now, thanks short creator, I'm actually mind blowned right now.
Edit: Damn... some people be saying in the comments "you SHoULd be uNDerrStandINg this ItS BaSIc?" For the record I understood it the moment I learned it (I have one of the highest grades in my calculus class), just not as fundamental as this, as to WHY it results in this as opposed to just remembering formulas then regurgitating it at a test. Now move along smarty pants, we get it, your oh so smart 🤓. Want a medal? Lol.
Bro just had awakening
Now imagine the anti derivative as the area under the curve but as a function of x and boom thats the fundamental theorem of calculus
@@aadi3319Bro just replied to a comment on a youtube short
@@aloedg3191 bro just replied to a reply to a comment on a youtube short.
blowned is wild
Including yourself as the "clueless" one is brilliant!
Why is that?
@@saginur4380I guess it'll be weird explaining integration to celebrities, so, the roles are reversed
this sh*t is better than my teacher's whole career
This is acc cold , make more 😂
Yessir 🫡
Goggins finished carrying the logs and now he's explaining them 💀💀
LMAO corn ball
Underrated comment.
My ex called me square so I times'd myself by 2
This is the most intuitive description of integration that I have ever heard. That question “sum of what??” points out what really matters. Real example of asking good question.
unironically, this actually made integrals make more sense, no other tutorial i saw actaully said that dx is the width, it may seem primitive, but it actually took me some time to understand
Goggins forcefully pushed that concept right into my head
David Gigagoggins-
Carry the logs❌
Explain the logs✅
Bro explande integration in a short better than my teacher in a 45 mins 💀💀💀
He didn't explain the part where you do the integral - he explained the beautiful theory of it.
It's ai
He's goggins for a reason
She actually never explained, I must ask the other faculty and he says is for bridges.
Integral from 0 to 0.5 of (x^2)dx =>
(x^3)/3 (x = 0.5) => 1/24
1/18*
No its 1/24 0.5=1/2 , (1/2)^3=1/2^3=1/8, (1/8)/3= 1/8x1/3=1/24
@ mb dawg
earlier - "frag it out"
now - "graph it out"
To anyone learning integration from this video:
As you make each strip or dx smaller, the approximation of the area under the curve is better.
Doing the calculation using integration techniques will provide infinitely small strips (dx) and will give you not an approximation but rather the perfect answer
David goggins is much better than my college maths teacher
That was the best explanation about integrals I have ever seen.
brain rot: ❌
brain grow: ✅
this explanation on integration is so easy to understand
waiting for more concepts.
Why have I never before heard such a clear and simple explanation on this topic ?
I love creators like you. People can’t learn math because of all the abstraction that’s been put into it - we needed someone to un-abstract it :)
Even his mental capacity is tough.Most people are afraid of maths but maths is afraid of him
David Goggins is now my hero
😮
It’s not him
Who is it?
@@Midnight_Blank-Slateai
@@Midnight_Blank-SlateUse of artificial intelligence, it has evolved ever since
Brooo Ty bro ima impress my calc teacher so much today
Bro i wake up and learnwd this mf concept
I really passed everything without having a clue what I was really doing
Bro explained it better than my teacher did in a whole year.
that was actually really well explained
The beat drop actually came in perfectly as soon as the realisation kicked in and I started understanding
Please do more Goggins videos
Had to rewatch the video coz that Patience Man was so good🔥
Please do one of Joey Diaz explaining triple integrals
Now we can not only see goggins carrying the logs but also him explaining it to us😂😂
But in all seriousness this is a really good explanation
Seen 5 or something of your videos. This is what content creation is all about. New things in the saturated platform. Learning with fun. Education niche never ever will get old unless it's some boring old ass classes. Keep rocking bro 🔥❤️
School teacher ❌
Online lectures ❌
David gogins ✅
Thnaks i know it now
So basically, what you do is do the opposite of a derivate ( i don’t know it’s name in English)
So X^2 becomes 1/3 X^3
Then you put it inside brackets and add the 0 and 0,5 just like in the vid but with the brackets :
[1/3 X^3] from 0 to 0,5 (i can’t make them little to the sides but it just like the video)
Then you replace X with the bigger number (in this case 0,5), and you replace again with the other number (0)
And you subtract the one with the small number from the one with the big number
So it will be : (1/3 0,5^3 ) - (0)
And ≈ 0,04 mu or i don’t remember the unit
And to convert it to centimetre square, what you do is 0,04 x ||j|| x ||i||
(Only those who knows will understand i don’t remember everything sorry y’all I’m bad at explaining too)
“Patience MOTHERF***R!” Got me dying 😂😂😂!
Ai David Goggins explaining math, I didn’t know how badly I needed this.
Calculus motivation GOES HARD
No way a 30 second short explained this better than most of the college teachers
Bro really thought he could get us with that AI 💀
It’s in the title bro..
Bro ain't so 🤓 @@cantripleplays
why are youtube shorts comments always so retarded
@@erenyayger3840 what the hell does bro ain’t so mean 😭
@@doonutholes 😔
Great AI skills you've got bro,nearly convinced me about Gogins talk about math 😂
so you add one to the power so x^2 becomes x^3
then divide by new power so x^3 becomes x^3 /3
now youve integrated it, you want to find the area under the graph between 0.5 and 0 on the x axis
so it's (0.5)^3 /3 - (0)^3 /3 which equals 1/24
and that's the area under the graph between those two x coordinates
Well that's more like memorization by you. Like adding one power and dividing by the new one. Kinda weird 😂
Do you know why the change in the indefinite of the function(here x² for eg) from the upper limit to the lower limit gives area?
That's the 2nd fundamental theorem of calculus and one thing everyone MUST know why but nobody knows it just hate on this great topic
That is not how you solve this integral..... You must diferentiate x2 and then solve until it matches one of the premade integrals.
@@ThorfinnBus nope I’m in y12
This person memorized rules. Exactly what you should do when learning maths. Good luck doing any type of maths without them. Unless your name is Isaac Newton of course.
@@RogierBe nah in topology and statistics you need creativity not rules
So glad I found this channel😂
Goggins stopped carrying the logs and started carry the 2
The natural logs
This is actually crazy, more of this pleasr
i’ll get this eventually 🙏
" *Who is gonna explain the log* " 🗣️🗣️🔥
From what i've learned, the "s" symbol he states is the symbol for the operation of antiderivative, as in taking the anti derivative of something, atleast from our teachers explaination. Though it being sum is a way nicer way of remembering what to do with it.
Another note: doing this will not give the exact area under a curve but rather an approximation of it.
Question: how is this formula practical in any stem field?
The s together with the dx is the simbol of the anti-derivative. But if you don't know the idea behind the notation, it will seem quite mysterious and arbitrary. Also you're leaving a lot of intuition on the table. This sort of pedantry from mathematicians is part of the reason why people find math difficult. They take a simple concept and explain in a way that is perfectly logical and formal but completely unintuitive. The thing is, the people who came up with calculus started from the intuition and then the formalism was developed over the following decades. And yet we teach it backwards. The same problem happens with teaching language; you get taught the grammar first, even though that's not how native speakers learn their language.
@@jessetallman2142 I may have learned calculus but do I know how to apply most of it to real world scenarios? Yeah that's a no, I really don't know what it would be used for atleast for the common public, but im sure there's a use for it somewhere out there.
@@amountedak9246 obviously the schooling didn’t affect your intellect. That wasn’t the question id you dont know what a stem field is i doubt youve stepped foot on a uni campus.
@@jessetallman2142 Maybe I just misunderstood the question though I do know what a stem field means, but you would still be right about me not having been to uni as that is just a plan for now. Field wise, i'm not really sure where it would be needed either as I haven't really done much research into what i'll be taking in the moment
The fact that he actually explained it better than my professor is actually sad
Honestly thanks I really needed this
Need to see more of this on my feed😊
I need David Goggins as s teacher
This genuinely helped me fully understand
ai goggins before gta6
I can't belive goggins answered my exact question i always had in math
Insane video bro..
Can i use it??
He explained better than most teachers
Bro now will dow marathon in maths 👁️👄👄💀💀💀🛐🛐🛐🗿
Thanks man I am a Architect this really helps alot while making my autocad files and all. 😊
😒
🗣️🗣️Graph it out man
😮Goggin integration concept more understandable than my math sir
Thnx
I fucking crying while reading intergration for hour!!! But now after the f exam... this vid pop up in the middle fuckin 3:20 AM?!!
Man why ;-;(yea i failing my additional math exam like fr)
He explained this in less then a minute that my teacher couldn't in a whole year.
Bro what episode is this from I never knew this man did maths too !
Its AI, if you are seriously asking
JRE #7300 bro ;)
most educational short, I have seen in my life
Bro gives the definition of an integral but doesn't answer the question
You could also use the trapezium rule, which is way longer but it’s still the same result(trapezium. Rule is an approximate though so it usually is a bit less than actual integration with limits). Furthermore, for trapezium rule you need to table out your x and y values and find distance between.
Trapez. Rule = 1/2 x width (y1 + y last + 2(y2+y3+…+(ylast-1))
It's actually easy, the integration of x² is x³/3 with limits 0 to 0.5 meaning
[(0.5)³/3 - (0)³/3] = 0.125/3 - 0 = 0.4166
i got that same answer
but i did it in my mind so i just mistakanly put the decimal wrong place😂
@@ChowDangFA Yeah it's a common mistake if you try to do it in a hurry.
0.125/3 is 0.04166..
@@karthik_8807 in calculas mathematics you can ignore decimals after the 100th place besides you can write 0.41667 for approximation
Bro that's wrong ans should be 0.0416 u placed decimal on wrong place
Bro brilliant very easy trick of integrating function
Lmaooo i thought it was real for a sec
Not quite as you will learn in advanced differential equations but I really like this explanation to learn about how to do integrations of functions without complex terms like imaginary numbers. I haven't really got it yet so I can't explain very well. 😅
Ai is getting dangerous hahahah
Its actually more general to just think of it as a sum, not necessarily an area, this will help when you start doing line integrals for examplr
Goggins can you please explain why don't you carry log 1
The worst thing to this is that it is explained far more clearly and easy to understand than any teachers at my school ever could... 💀
Listen man. Create long form AI videos to explain maths concepts.
Its really effective at explaining.
It bet this would blow up
Genius idea! Perfect explanation! Thank you!
Correct me if I'm wrong. So does it mean that rhis is explaining the average differences compared to the direct differences of each distance?
Not really though.. it’s not the average but rather taking smaller parts (or rectangles) and adding them up to find the sum of all parts or in this case to find the approximation of the area under the curve between these given values and this given function. That’s why it’s also known as the Riemann sum. But hey I could be wrong too. 😅
It’s actually the limit as n goes to infinity of the sum. This allows those boxes on the screen to be as close to the actual function line as possible. 👍🏼
That's how the new generation gonna learn smh
just be grateful this guy is teaching calculus that can be understood by 10 year olds 😭😭
Best short i ever watched
0.125/3 is the result
Freaking prodigy in the comments section
@@yuvalkoren4070 whats a prodigy?
@@mihaleben6051 a gifted child, just a joke though😊
@@yuvalkoren4070 oh. Either way you mean that, i agree
I got the formula from desmos. I perfected it until the numbers were right
It is x^z+1 - y^z+1 /z+1
Where z= amount of x in the int
So using this, int(2,1,1)=1.5
@@mihaleben6051 a bit complicating stuff, it's quite standard, highschool level at most.
The integral itself is x^3/3 and then the final solution is (0.5)^3/3=0.125/3
The answer is 1/24, if anyone is curious.
No it's 0.4166666....
@@ShipraDeyBhowmik-zk2sg 1/24 is the same as 0.416666
@@emas695no
@@ShipraDeyBhowmik-zk2sgnah you have done it wrong my friend
@@うちはしゃりんがn I know 😂😂 my fault 😂😂 science and mathematics are some of the things where even Einstein is wrong if he's proved to be 😂😂
2 more short like this i might surprise my math teacher
so blessed i don't need to understand this
This creator is doing a wonderful job, congratulations from Bharat 🇮🇳
1/24? Answer
Yes
Same here!
Yeah that’s what I got
Greatest crossover of all time.
yeah we’re doomed
Education must be available to every type of person. Even the people who enjoys these types of brainrot.
@@zqtc4114😂😂. Yeah this was hilarious though
Dude you are doing god's work rn 🔥❤
The answer is 0.25
You're wrong. (1/3)x^3 would be the antiderivative. Then you'd plug in .5 and plug in 0 and subtract those values. Which would get .04167
@@GodToaster1/24 if you’re being exact tho
@@GodToaster shouldnt it be 1/2*x^3?
@@trevortornik1589nah the reciprocal is taken from the exponent after it is changed so since it becomes x^3 the coefficient is 1/3
@@trevortornik1589 Ya like sloosh said. I think you are mixing together derivative and integral power rules
the dx explanation help a lot