it seems so obvious its amazing it took us so long to make this connection. I think props are in order for Descartes for making the connection between geometry and algebra so easy to see. Newton gets a lot of credit, but Descartes really set it off IMO
integral of the derivative of f(x) =/= derivative of the integral of f(x). The indefinite integral of any function always includes adding a constant because the the derivatives of x^2 + 5 = the derivative of x^2 = 2x. So, when you integrate 2x you have to add a constant (c).
Nah, it doesn’t work both ways Differentiating an integral of a function gives you the function itself while integration of a derivative gives you the function but the constant part stays undefined. Being a nerd for a lil
It actually doesn't work for differentiating an integral too. For limits of some constant to x, say from 0 to x or 1 to x or whatever, it will work. But to be precise, you should apply the leibnitz rule. (I can't type that here lol, so Google it). Being a nerd for a lil
@@parikshitkulkarni3551 I’m not sure why Leibniz rule wasn’t taught in my calculus classes. It’s a very underrated rule for evaluating hard definite integrals. Physicists know it as Feynman differentiation, because he popularized it I guess.
Your meaning is correct but the terminology is not. Differentiation is a left-inverse of anti-differentiation. and anti-differentiation is a right-inverse of differentiation. Integration, on the other hand, typically gives back a number rather than a function. If you set the limits of integration in a particular way, though, it can be a (two-sided) inverse for _some_ functions.
You can. There's no problem with doing that. Because the fact is definite integral of xdx from a to b is same as tdt from a to b is same as pdp from a to b. And this is because at the end of the day, after integrating the integrand, you're going to simply put the limits in. So in this case, integral of 2xdx from 0 to x will be same as integral of 2tdt from 0 to x. Which will simply be [t²] from 0 to x, which will be x²-0 which is x².
Yep, still the same. d(x^2 + C)/dx is still 2x. The constant C is only a vertical translation of the graph; the slope at any point on the parabola x^2 will still be 2x, irrespective of where it lies on the y-axis. Bit fast and loose, perhaps, but it should point you in the right direction.
Imagine if the original function was x² + 2. If we differentiate that, we would get a derivative of 2x, but the integral of that 2x wouldn't give us x² +2, sooo is differentiation really the opposite operation of integration. This is just a question I still haven't learned integration in school so I don't really understand this completely.
What if we don’t start with zero? Let’s say we start from c. It’s pretty obvious how it works when we have right triangle, but what if the function is a curve? What do we do now?
Yes. But these videos don’t really teach you that. Derivatives and integrals are rigorously defined and computed by evaluating limits. In a calculus class you start with the limit definitions and use them to compute the derivatives and integrals of simple elementary functions (think most of the functions encountered in algebra classes like polynomials, exponential functions, logarithms, radicals, trig functions, inverse trig functions, etc). Once you have a comprehensive list of derivatives and integrals memorized or tabulated somewhere for later reference, you begin learning rules and tricks to calculate derivatives and integrals for more complicated elementary functions. Some examples might be x^4*cos(x^2), sec(x), e^x*sin(x), cot(x), x*ln(x) and so on. Derivatives of well behaved elementary functions in general are pretty straightforward to calculate using things like product rule, chain rule, quotient rule, etc. Depending on the function it can get long and messy but if you know your derivatives of simpler elementary functions it’s just a bunch of algebra and simplification mostly. Integration in general is much harder, and there is no guarantee an integral of a elementary function can be expressed in terms of elementary functions with a finite number of algebraic operations, i.e. addition, subtraction, multiplication and division. But for ones you can solve like that, you learn tricks like, clever algebra manipulation, u-substitution, integration by parts, trig substitution, partial fraction decomposition, etc to turn a more complicated integral into integrals we already know. If you actually want to learn how to do calculus, I recommend not watching oversimplified AI shorts. Books, lectures, and long form content are the way to go.
In all seriousness, these explanations are incredibly well made....with the examples and animations and everything.
If she was my maths teacher,I will get a perfect 100 in biology
Ye
biology 🗿
💀
we doing class reproduction experiments with this one
@@rroy1985
😟😟😟😟😟😟😟😟
it seems so obvious its amazing it took us so long to make this connection. I think props are in order for Descartes for making the connection between geometry and algebra so easy to see. Newton gets a lot of credit, but Descartes really set it off IMO
what abt Pierre De Fermat.... the goat
Lol IMO at the end stands for INTERNATIONAL MATHS OLYMPIAD 😂!
integral of the derivative of f(x) =/= derivative of the integral of f(x). The indefinite integral of any function always includes adding a constant because the the derivatives of x^2 + 5 = the derivative of x^2 = 2x. So, when you integrate 2x you have to add a constant (c).
This is genuinely the best explanation to a lesson i've ever seen. i've never studied the intergals thingy or calculus and i understood it. wow
Why tf is kim kardashian teaching me integration 😭
Bro gen x,y whatever the fuck the new one is gonna be learning a whole lot from this wtf 💀💀💀
Gen x is middle aged and gen y is millennials 💀💀💀
I mean they are your parents and brothers only 😅
Kids are called gen alpha today.
gen x²
@@yttyw8531now gonna gen beta
hawking saying yes bruddaaaa made my day
Talking stephen hawking is wild
"Let's just show him an example. Listen bro, yes bredaa" - Dr. Hawking
Bro made Stephen Hawking talk .
WTF😮
Man wtf! This moment was an epifany!!! Amazing explaining skills!!!
This channel is awesome, keep up the good work :)
That horse-man image is wild 💀💀
Beautiful! More please!
Wow this is the first time I’ve ever seen an explanation for the Fundamental Theron of Calculus, good vid 👍
God, This gives more experience in Maths Now then I had When I was in High School.
Make a full video on integration and differentiation
Listen bro😭
Yes brotha😭
You can't help but be amazed by the beauty of maths!
A highschool math playlist please
Nah, it doesn’t work both ways
Differentiating an integral of a function gives you the function itself while integration of a derivative gives you the function but the constant part stays undefined.
Being a nerd for a lil
It actually doesn't work for differentiating an integral too. For limits of some constant to x, say from 0 to x or 1 to x or whatever, it will work. But to be precise, you should apply the leibnitz rule. (I can't type that here lol, so Google it).
Being a nerd for a lil
@@parikshitkulkarni3551 I’m not sure why Leibniz rule wasn’t taught in my calculus classes. It’s a very underrated rule for evaluating hard definite integrals. Physicists know it as Feynman differentiation, because he popularized it I guess.
ain’t no way this was the video that help me understand this theorem 😭
derivatives are invers of integrals, but integrals aren't inverse of derivatives. d/dx(x)=1 but int(1)dx=x+C for C real number.
Your meaning is correct but the terminology is not. Differentiation is a left-inverse of anti-differentiation. and anti-differentiation is a right-inverse of differentiation. Integration, on the other hand, typically gives back a number rather than a function. If you set the limits of integration in a particular way, though, it can be a (two-sided) inverse for _some_ functions.
I love this series
Integration is the inverse of differentiation and vice versa.
This man is doing God's work
Learning math like this would end world hungry👌
C : "Don't you remember?~"
You cannot use the variable x as endpoint if it's already in the integrand.
You can. There's no problem with doing that. Because the fact is definite integral of xdx from a to b is same as tdt from a to b is same as pdp from a to b. And this is because at the end of the day, after integrating the integrand, you're going to simply put the limits in. So in this case, integral of 2xdx from 0 to x will be same as integral of 2tdt from 0 to x. Which will simply be [t²] from 0 to x, which will be x²-0 which is x².
@@parikshitkulkarni3551 So if F(x)=1∫x xdx, then what is F(1)?
Good mashup
Oh, so it's the real Hawking voice the whole time 😲
When Stephen Hawking said listen bro I listened
Integration is not the inverse of differentiation. The boundary is
Yes Brudda
Why is Hawkins' mouth moving??
Hawkings was one of the brightest minds
I think I wanna into Maths & Statistics degree
But what about( + C)? Genuine question, is the integral of the derivative really the same when we get + C?
integral of the derivative of f(x) = f(x) + C so you're right!
Yep, still the same. d(x^2 + C)/dx is still 2x. The constant C is only a vertical translation of the graph; the slope at any point on the parabola x^2 will still be 2x, irrespective of where it lies on the y-axis.
Bit fast and loose, perhaps, but it should point you in the right direction.
thanks i understand now
Imagine if the original function was x² + 2.
If we differentiate that, we would get a derivative of 2x, but the integral of that 2x wouldn't give us x² +2, sooo is differentiation really the opposite operation of integration. This is just a question I still haven't learned integration in school so I don't really understand this completely.
What website does he use to make these?
What if we don’t start with zero? Let’s say we start from c. It’s pretty obvious how it works when we have right triangle, but what if the function is a curve? What do we do now?
Omg Kim is smart
Unrealistic. Stephen Hawking is moving his mouth
HAVE TO ADD C THE CONSTANT OF INDEFINITE INTEGRATION
Stephen hawking's mouth is moving, even speaking in American English
the robotic voice isn't robotic enough.
what happens if the area is a square?
if the integral is 8x
why hawking moving his mouth?
Wtf with that random ahh "cap" 😭😭😭😭
I'm actually learning from brainrot 💀
Can someone explain this to me i tried using 5x³ and diffrentiated it to get 15x², but now 15x²*x/2 dosent get you 5x³,it gets u 7.5x³?😂😅
yo bro integrating 15x^2 gets you 15x^3/3 +c, so 5x^3 like you started with
You divide by the power + 1 so you had 15x^2 so 15x^2+1/2+1 = 15xx^3/3 = 5x^3
@@onlocklearningwhy dividing by 3?
@@jokerstone3524ohhhhh ty
Nvm ty
Bro forgot the +c, that graph could have been anywhere
yes bredda
Why is the height y
Not that easy in the general cases. Like there are function such that they are not the integration of their derivation
where you find this math lady 😂
The world knows Kim don't do math
Can we solve the damn thing without graph 😕
Yes. But these videos don’t really teach you that. Derivatives and integrals are rigorously defined and computed by evaluating limits. In a calculus class you start with the limit definitions and use them to compute the derivatives and integrals of simple elementary functions (think most of the functions encountered in algebra classes like polynomials, exponential functions, logarithms, radicals, trig functions, inverse trig functions, etc).
Once you have a comprehensive list of derivatives and integrals memorized or tabulated somewhere for later reference, you begin learning rules and tricks to calculate derivatives and integrals for more complicated elementary functions. Some examples might be x^4*cos(x^2), sec(x), e^x*sin(x), cot(x), x*ln(x) and so on.
Derivatives of well behaved elementary functions in general are pretty straightforward to calculate using things like product rule, chain rule, quotient rule, etc. Depending on the function it can get long and messy but if you know your derivatives of simpler elementary functions it’s just a bunch of algebra and simplification mostly.
Integration in general is much harder, and there is no guarantee an integral of a elementary function can be expressed in terms of elementary functions with a finite number of algebraic operations, i.e. addition, subtraction, multiplication and division. But for ones you can solve like that, you learn tricks like, clever algebra manipulation, u-substitution, integration by parts, trig substitution, partial fraction decomposition, etc to turn a more complicated integral into integrals we already know.
If you actually want to learn how to do calculus, I recommend not watching oversimplified AI shorts. Books, lectures, and long form content are the way to go.
@@jacobharris5894 wow thank you so much, I would love to have you as a someone I can discuss some problem maths
What a g
Ur the be(a)st
+c
Defeating the matrix as sorce means the mind takes all knowledge now what is the formulation primal
sigma
cap lol
Wtf is this braingrow
Les be honest feels weird seeing someone using Stephen Hawking (AI) in a video after what came out in the (Ep$t@!n)documents
do you think this video is gonna make the ghost of stephen hawking jump out the screen and touch more kids. stop being a snowflake
Bro it wasnt actually stephen hawking 💀💀💀
it was someone else named stephen hawking not this guy (they have the same name so people joked about it)
hi can I have your discord?
bro I just made one discord.com/invite/PgffddTXDY
@@onlocklearning demn thanks man lemme join it