@@MDArslan-pt6yp you sound stupid, functions have nothing more to do with calculus than they do with the rest of mathematics (algebra, linear algebra, geometry and so on)
@@ejsans2059 yea that's the point it's just that some people think you're stupid if you Find that learning it from a kids perspective is Easier which is dumb
i am 43 , thats almost how my teachers explained this, but there is a catch , you can not define polygons with it ... which means you would use semi circles.. for math; u need to get an exact answer ... you can not do it with ... this is a simple explanation but this is not calculus.
This is honestly how our teacher explained it! All the formulas were still confusing but he explained it really well, better than the teachers who taught us long division in primary even.
This should be how the teachers and college professors go about explaining what calculus is in the very first day. This makes it much easier to incorporate irl scenarios
Yeah but first thing of calculus is derivatives which has similar concept but this concept won’t be directly used until integrals. There’s probably a better way to introduce than this one imo
They could show you, but you wouldn’t know how to calculate it until halfway in the class and by then you would have forgot this 1 minute demonstration. If anything, teachers do show this idea to students when they teach integrals. That’s the whole foundation, when you learn Riemann sums first half way through the class
Don't they teach you this on your 4th or 5th grade using a graph sheet? Or do they teach you integration at 4th or 5th grade? I only started learning integration in my 11th grade.
I do remember learning something like this at some point but I immediately forgot, especially as soon as the actual calculations started. I can remember it if you give me something visual like this but if you give me a whole month of calculations with pretty much no diagrams or whatever there’s no way I’m gonna understand what you’re talking about
But it doesn't teach anything. HOW do you count an infinite number of rectangles?? and if anyone says, "well you just..." Well that's not in the video.
I am well past the age I should know this stuff, and have always struggled with mathematics. This video has taught me so much compared to half of the videos on this website!
ugh, i miss math. i don’t like endless or busy-work-feeling homework, but i wish i had the time and money to just keep taking random classes forever cause i just like learning
@@lannister3320 not the point, the heart of a modern calculus class is limits, and to understand modern calculus you need limits because pretty much all of the proofs for calculus involve using limits.
@@sajalmittal.limits, differentials, differentiation, advanced algebra techniques, series, vector math, calculus with vectors. Integrals are like 1/10th of all of calculus lol you smokin something bro
@@sloosh2188 dude ik but what's the use of that all complex calculations being a physics major I don't find myself doing 10 pages of differential and integral calculus for a concept application🦅
Except this video isn’t really teaching anything... It’s just a demonstration. You still don’t know how to calculate the infinite sum without first spending a few weeks learning Riemann sums and integration techniques. If anything, it’s also an insult to the students spending weeks of hard work to learn something just to call it as easy as a 1 minute video… You must not have taken Calc because this isn’t even the tip of the iceberg
She actually explained Riemann sums which will always be an approximation of the area. The definite integral would be the exact area of the curved pool.
@@liamferguson4199 yeah I know for example if we did definite integral of sin x from 0 to 2π but if we find area enclosed by curve with x axis it will be 4 sq units
@@masonv9333 that is also true no argument there🫡. I will say, after going through all the uni upper level math courses offered at my school; past calc 1, I have yet to use a Riemann sum to calculate the area of some irregular shape, paraboloid, or ellipsoid. Just too much work.
Some of these comments make me sad😔. People really out here not caring about Calculus or putting the effort in to understand the beauty of it. The other half of the comments had terrible teachers, which is even sadder.
@@sveps8883 bro why in the first place would you explain calculus to a 10 year old, there is a reason why calculus is taught college and high school, at 10 years the kid should be enjoying life, and playing, rather than this trauma
Im 11 and i know simple intregation, derivatives and simple limit proof (epsilon -delta) . Source of knowledge?: bprp,organin chemistry and prince newton ( these three are the main source there are more)
@@baronvonbeandip this point makes sense until you come across a kid like me who struggled with math badly and doesn't know how they passed algebra or any high school math for that matter because they still have no idea how to do them. I haven't taken a math class since high school. so thankful that I didn't have to pass calculus to get my high school degree. That sounds like torture
@@baronvonbeandip Algebra and Coordinate Geometry except binomial applications and complex numbers. You need to understand the fact that calculus requires a mature brain to understand concepts and exceptional manipulations which takes time. That's the reason it is taught in grade 11th followed by trigonometry in grade 10. It is what it is🤷🏻♂️
@@alclay8689 Calculating the rectangles would be a discrete sum. Calculating an infinite amount of infinitely small rectangles would be a continuous sum. The discrete sum is an approximation of the continuous sum,
@@Daniel31216 oh I get that. She didn't explain how to do any of that in a calculus way. All she said was make smaller rectangles and calculate the areas. That's just algebra. If I did that on an exam my professor would've had the engineering dean throw me out of college lol. Y'all are trying to do calculus without any math and I'm not gonna sit here and pretend like she nailed it.
@@alclay8689she’s explaining it to a ten year old what did you expect for her to pull out full integrals this is just a basic concept and understanding
This is a pretty small but also pretty fundamental concept in calculus called integration, and the method she used is called a Riemann sum Another pretty fundamental concept would be derivation, which is basically just plotting the rate of change of a graph over time Another key concept is realizing that integrals and derivatives are actually inverse operations of each other, like addition to subtraction or multiplication to division Professor Dave Explains has some really great videos you can check out if you’re interested
To all those gen alpha mfs who cant understand anything without the brainrot heres the translation: if a pool has an shape which is a rectangle, The area (skibidi) of the rectangle will be: Skibidi= Fanum×tax. Length = fanum, Breadth = tax. And if you did the equation you will the area (skibidi). But if the pool's shape is kinda weird and it isnt like a rectangle you can just use small rectangles till it completely covers the pool. If you take the area(skibidi) and add it all up. You will recieve the pools area. Approximately it will be Same not fully Correct.
Thank you for explaining that. I am NOT a math person, and understanding what the heck all this stuff is for what it does is so important. If someone had explained this when I was looking at my college course requirements maybe I would have tried the science track I abandoned.
This is a very poor explanation. Maybe I just deal with smarter 10 year olds, but I would show them more directly what it does. And I wouldn't get into pool inferences about integration. Those poor kids, then they finally are taught calculus. Their first reaction will be: this is nothing like the pool boxes!
I was unable to continue taking calculus this year but I need the knowledge for uni so I'm just self studying it. Well I'm trying but I've been procrastinating 😅😂
This is basically explaining Riemann sums which is how integrals are first taught. Technically calculus starts with derivatives and integrals is calc 2. This is just how calculus is always taught though.
You learn limits first tho. Then derivatives and the first pinciple rules of differentiation with limits and then reversed process called integration. Then you are taught to change the functions into a suitable form and eventually when you go mad they introduce new bullshit that you never thought existed
What calculus teacher doesn't explain this way of approximating areas with Riemann Sums?....There is a very important missing part to this explanation too...And that is how to find / calculate the sum of the areas of all the infinitely many tiny rectangles using "antiderivatives" which is called the fundamental theorem of integral calculus....So she only gave part of the story actually....but yeah that is the way it is usually explained in any calculus 1 class.
@@anumitapandit1672 You can calculate the area of top of the pool using integration (Green's theorem would be the most useful). You then multiply that area by the depth.
There is no benefit in explaining this to a 10 yo. This only covers a part of the concept of integration, and even if they understand what you are saying, they will not see the importance of differentiation, because you didn't actually solve any problem. You should always start with Euclidean geometry, and only then move on to calculus. Calculus is an advanced concept, no matter how you look at it.
Yeah she made it simple. It's definitely easy, only if you understand the basic concepts. And that's not all of calculus, those are integrals. Derivatives are a bit easier than that. But are a harder concept to grasp as it requires you to know what a function is.
Why do schools insist on teaching algebra BEFORE geometry? Horrible mistake. Fortunately, Einstein had a math teacher early in his education who saw that while young Einstein was not good at algebra, he was EXCELLENT at geometry and so skipped algebra🙏
I don't know what your experience was, but there were plenty of times I needed to know algebra within the class called geometry, and I would've been completely lost if I hadn't learned what a system of equations, or a quadratic formula were, prior to taking geometry.
@@carultch those should be taught in the context of geometry class. When those algebraic formulas are applied in geometry they make much more sense to visual-modelng learners
Let's suppose the two halves of the pool are given by: y1 = x*(6 - x)/5 y2 = 1/30*x*(x - 3)*(x - 6) where x goes from 0 to 6 The height of each rectangle is given by y1 - y2: y1 - y2 = -x^3/30 + x^2/10 + 3/5 * x The width of each rectangle is the infinitesimal dx. So we add up (integrate) the expression (y1 - y2)*dx from 0 to 6. For polynomial terms in the form of k*x^p, the rule for integration is the following: 1. Boost the power (p) by 1 2. Have the new power (p+1) join the coefficient downstairs. 3. Thus, each term becomes k/(p + 1) * x^(p+1) 4. Repeat for the other terms, and include the arbitrary constant C at the end Thus, our result is: integral (y1 - y2) dx = -x^4/120 + x^3/30 + 3/10*x^2 + C Keep it simple, let C = 0. Evaluate at x=6, and evaluate at x=0, and subtract the later from the former: 1/10*([-6^4/12 + 6^3/3 + 3*6^2] - [-0+0+0]) = 7.2 units^2, final answer.
