Its odd how every "Intro to Calculus" video I see fails to define exactly what it is. I remember Day 1 of AP Calculus, the teacher drilled it into our heads: Calculus is the mathematics of motion and change.
That’s really funny actually because I just watched a video that’s supposed to serve as an intro to the idea of calculus and one of the first things it said was how calculus is the math of change. (first calculus video I’ve ever watched too lol). I guess you just gotta find the right one.
I was brushing up on my calculus today with The Organic Chemistry Tutor, and his explanation helped connect the dots for me that my professors did not explain. Derivatives shows you the predicted instantaneous *rate/slope* at a given point; integration shows you the *area* at a given section of an equation. My assumption after learning calculus 1 and 2 was that derivatives were only used to prove that integrals work, not something tangible. Once I understood that vital connection, the word problems suddenly made a lot more sense and why I sometimes used one versus the other.
Motion and change is one application of calculus, and usually the easiest motivating example to use for introducing the topic, but it isn't the only application. Finding areas of exotic shapes is another application. There are also applications in subjects like statistics that have nothing to do with motion.
That’s literally me in AP calculus. It can be fatal not to right everything down sometimes so I just have a habit of writing everything the teacher says and writes
@@shami9773focus on bits of information at once and understand the fundamental theorems. as someone who’s gotten to multivariable calculus in college (I also took AP Calculus in high school) just practice, practice, practice.
Ephesians 6:10-18 says, Finally, my brethren, be strong in the Lord, and in the power of his might. Put on the whole armour of God, that ye may be able to stand against the wiles of the devil. For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places. Wherefore take unto you the whole armour of God, that ye may be able to withstand in the evil day, and having done all, to stand. Stand therefore, having your loins girt about with truth, and having on the breastplate of righteousness; and your feet shod with the preparation of the gospel of peace; above all, taking the shield of faith, wherewith ye shall be able to quench all the fiery darts of the wicked. And take the helmet of salvation, and the sword of the Spirit, which is the word of God: praying always with all prayer and supplication in the Spirit, and watching thereunto with all perseverance and supplication for all saints. The bible is no old book. You have to really let Christ open your eyes; to see the world in shambles. Many people say it's a religion to lock up people in chains, and say it's a rule book.. why? Because people hate hearing the truth, it hurts their flesh, it's hurts their pride, it's exposes on what things have they done..people love this world so much, s*x, money, power, women, supercars.. things of this world. Still trying to find something that can fill that emptiness in your heart. You can't find that in this world.. only in Christ, the bible is no chains, it's a chainbreaker. Breaking your sins into pieces... Repent now, and turn back to the true Lord only.. God bless. 😊😊😊
Emphasize why Calculus is so awesome in one minute. The understanding part is hanging out somewhere else in a mysterious place. Math teachers aren't good at explaining math because they are too excited about being good at math to have to explain it to those who are not. It's an inverse proportional equation. What happens is that students who are bad at math only hate math until they become good at math. The one's that make it, end up loving math; the one's that don't continue to hate math. It's like a cult that once you join, you go: I see that now.. it's all so logical. But the one's that don't, continue the underground movement of hate against math. Very few, if any math geniuses understand why math is so hard to many people. They only seem to understand why it's so simple to them. The true genius understands both simultaneously. Good night.
Most people who are good at things naturally tend to not understand how others are unable to do them also. If you are naturally good at something you do not think about how you learned it. That applies to all things. Sometimes, people are blessed to understand that others see or feel things completely different from themselves. They try to think how others are thinking and how they can guide them to being able themselves. Those people are rare.
same with tech (hardware/communications and programming/networking) teachers and classes. some of these teachers just zoom through the material and just marvel at how genius they are themselves but just leave most students behind. funny that i learned one very important thing from my breakdancing buddy who is now a teacher at a college...but he told me this over 10 years ago before he was a teacher. "you dont truly understand something until you can EASILY teach it, and people get it". but then u can talk about it still on a higher level with people who are very experienced/educated.
So basically breaking down a shape into smaller pieces again and again until it matches with the area of the shape then use the formula on each shapes that you broke down and you can add that up and get a accurate estimated area CALCULUS IN A NUTSHELL
While it seems too easy just remember: integrate to find area under the curve. That x^2 might represent the weight of a cable. The integral, then, is total weight between two supports at 2 and 5.
@Prodigious147 thank you, I think. But, no, I'm not gpt. I vividly recall when I first learned how complicated problems like suspended cables could be easily calculated with calculus....
I feel like there's more than enough space to write the rule Integral of Xⁿ=(Xⁿ⁺¹)/(N+1) to get X³/3 to give beginners an easy win. If you're looking for ideas, your next short could calculate just how much space.
@MrUndersolo Nah, not really, except for my comment about there being more than enough space to add the formula. There are no free rides in math, but it gets easier if you learn the basics of the game. That means anyone who wants to understand this video must understand basic algebra, but if you don't include that formula they won't have a chance.
Hello sir thanks for teaching the concept…I want to know one thing is there a way the Area under the curve of a random graph meaning if we don’t have the function for it and it doesn’t follow any pattern either. Thanks and Namaste 🙏
You can estimate the area: x = 2->3 y = 4->9 av = (4+9)/2 = 6½ x = 3->4 y = 9->16 av = 12½ x = 4->5 y = 16->25 av = 20½ So the estimated area Ae = 6½+12½+20½ = 39½ not bad. The estimate is obvious too high because of the curve of y = x² ... the real value of y(2½) = 25/4 = 6¼, not 6½ Now again with real values: y(2½) = 6¼ y(3½) = 12¼ and y(4½) = 20¼ with a total estimated area Ae = 6¼+12¼+20¼ = 38.75 Getting closer to the real area. Making more and smaller steps in x will result in better estimates. Using a computerprogramm or Excel sheet will do the trick without integration.
@@BingeBaconShortz For this equation it is better to integrate the function. But with very complex equations estimating is really a good choice to find an answer close enough to the analytic answer.
Here's the step-by-step solution to find the antiderivative of x^2: Given: f(x) = x^2 Step 1: Apply the power rule for integration. ∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration and n ≠ -1. In this case, n = 2, so: ∫x^2 dx = (x^(2+1))/(2+1) + C Step 2: Simplify the expression. ∫x^2 dx = (x^3)/3 + C thank you chat gpt
So why exactly are we multiplying the Xs 🤔 subtracting the x points ,dividing by 3, then dividing both sides both times the x points 🤨 and then subtracting them 🤔
3 semesters in the classroom and still don’t get it. Professor was generous with the C-. Should have failed me so I could get a do over in summer school.
Love your high hopes and enthusiasm but it’s important to be realistic! If you put in the time, you can understand the basics in a month or so but to understand what’s truly happening, it’s important to grasp, geometry algebra, and trigonometry before you start your calculus journey! Best of luck in your math endeavours! -An AP Calc B/C student
Oh cool, I am also trying to learn calculus so I can use it for physics, I don't think that there are AP courses in my country. Otherwise I wouldn't learn it, because they do not teach it before really high levels of education in my country. Also I am 7th grade in my country which is 8th in USA lol.
it's some rule you will learn, dw about it for now. you add one you add one to the exponent x^2 + 1 = x^3. the three you see is from 2 + 1. The 2 is the squared that's why it's 2
@hiddentymesLegendary …since this is an area problem he should point out that the square units must be included with the answer. In this case the units are arbitrary since none were specified. So each of us can choose to give whatever units each of us desires. Since we weren’t given any particular units, I could call mine square feet. You likewise may choose to call yours square meters… and on and on, for whatever units each of us chooses, since he didn’t specify any particular units.
@@hiddentymesLegendary …far be it from me to speak ex cathedra, but to my scant understanding of the subject of calculus, the whole idea of integral calculus is integrating functions that are integrable, and differentiating functions that are differentiable. That is, a function must first be continuous, therefore discontinuity is a factor, their limit must exist, and other crucial factors, etc. Some, for reasons due to such factors must be integrated piecewise. So it seems, to me at least, that your question is somewhat self contradicting. I say that respectfully. But a curve, that is, a function must first have an equation in order for it to be differentiated or integrated.
Then at some places I saw that with calculus we can find the area of any curve . That means we can't find the area of every curve? Or any shapes bounded by curve?
@@hiddentymesLegendary A curve must first be a function. A function must have an equation which can then be integrated or differentiated. Given any curve that meet those basic conditions and obey a few other restrictions then any of “those” curves can be integrated. Some equations, or functions, or curves, can’t be integrated or differentiated on some intervals of their graphs due to lack of continuity, or discontinuity, for example. Area under some curves have to be approximated by additional techniques in calculus. If I drew some random curve without fitting an equation to it, it couldn’t be integrated or differentiated. If we drew some random curve on a graph and bounded it from 0 to 3, say, but had no equation for that curve we couldn’t integrate or differentiate it. Equations for functions, or curves, can be built from data, but that’s beyond my ability to discuss at this point. So… yes, any and every function, or curve, using those terms interchangeably, that meets the requirements that enable us to differentiate or integrate it can be differentiated or integrated.
Literally this is not only explaining how calculus is so simple but why we even do it actually so simple. Why aren't we taught it like this? I think we taught it in like a way that's rushed to get as much information in but it's not even that much information to just say why we do it and just so easy
One way you could do it, is with Simpson's rule. This is a method that gives more computational efficiency than the standard Riemann Sums they teach you, when laying the groundwork for understanding integrals, in the prologue to calculus. Simpson's rule constructs parabolas among each group of three data points, so that it samples a representative position, slope, and curvature, of the shape, that then varies throughout the shape's domain. The formula for Simpson's rule is set up so that you don't even need to think about parabolas to use it. This is what you'd do if you were given a shape and could measure data points to figure out what the curve is, but didn't know what mathematical function defined those points. One place you might see this, is the way CAD software estimates the volume of exotically shaped parts.
Math explanations always assume you know a certain level of math and I always get caught up on little unexplained parts. I can’t learn from an explanation if I don’t know where numbers are coming from.
What the flipper doodles is that 1st symbol on A=__x2 dx …and how did it get to x3!? I get the division part because it’s automatically multiplication..im just lost
The funky S-shaped symbol is an elongated S called an integral sign. It means a continuous sum. The dx refers to a dinky change in x, that is infinitesimally thin. The way that x^2 turned into x^3, comes from the power rule. In general, when you do the reverse process called differentiation, an expression in the form of k*x^n, turns into n*k*x^(n - 1). In other words, you leave the original coefficient (k) alone, and have the existing exponent (n) join the coefficient. Then you reduce the exponent by 1, so that it is now (n - 1). There are limit proofs of this rule you can look up, but in general, it comes from the binomial theorem of expanding (x - h)^n to show this from first principles of how we define the derivative. To reverse this process for integration (which the fundamental theorem of Calculus proves is connected to derivatives) we reverse the formula, and get k/(n + 1) * x^(n + 1). So leave the coefficient alone, increase the exponent, and have the new exponent join the coefficient down below. Do this for x^2, and we end up with 1/3*x^3. Plus an arbitrary constant if applicable, as we do for unbounded integrals in general.
Basically calculus in all about the tangent line. As you might have remembered from Algebra 1 it uses a more complex version of the point slope form quotient which becomes the secant quotient and then the tangent quotient to find the limit and then this becomes the deifference quotient and this gives you the derivitive and its opposite cousin the integral. Then there is the shortened version of the difference quotient dx/dy and the rest in a lot of algebraic manipulation. I took it one time and failed miserably but what I didn’t realize is how much I learned in the process of failure. I have been going over the material again before I retake it and have found that my real problem wasn’t the calculus part of the course it was my failure to intuitively understand college algebra and trig. It’s so cool that if you fail it you might be in love with its complexity like me and be ready to retake it. One thing that makes it cool is the incredible applications of calculus which include space travel. That might get you hooked so Google it and then you can find you are doing simpler but the same basic math they used at NASA to put a man on the moon and the pathfinder on Mars. What kind of smack can you talk about that!
Its odd how every "Intro to Calculus" video I see fails to define exactly what it is. I remember Day 1 of AP Calculus, the teacher drilled it into our heads: Calculus is the mathematics of motion and change.
That’s really funny actually because I just watched a video that’s supposed to serve as an intro to the idea of calculus and one of the first things it said was how calculus is the math of change. (first calculus video I’ve ever watched too lol). I guess you just gotta find the right one.
Been out of high school for years and I’ve been looking for this cause I love math. Thanks. Ur a legend.
I was brushing up on my calculus today with The Organic Chemistry Tutor, and his explanation helped connect the dots for me that my professors did not explain.
Derivatives shows you the predicted instantaneous *rate/slope* at a given point; integration shows you the *area* at a given section of an equation.
My assumption after learning calculus 1 and 2 was that derivatives were only used to prove that integrals work, not something tangible. Once I understood that vital connection, the word problems suddenly made a lot more sense and why I sometimes used one versus the other.
Motion and change is one application of calculus, and usually the easiest motivating example to use for introducing the topic, but it isn't the only application. Finding areas of exotic shapes is another application.
There are also applications in subjects like statistics that have nothing to do with motion.
Thank you!
First principle of Calculus:
Calculus is Awesome 😎
Me: got! Let me write that down.
That’s literally me in AP calculus. It can be fatal not to right everything down sometimes so I just have a habit of writing everything the teacher says and writes
@@shami9773focus on bits of information at once and understand the fundamental theorems. as someone who’s gotten to multivariable calculus in college (I also took AP Calculus in high school) just practice, practice, practice.
@@shami9773although mindlessly writing without understanding can be just as fatal
@@toastycrystaleclxpse3423writing without intention to further study your own notes is worse
Definitely write that down, folks - it will be on the exam!
Hell yes a bunch of numbers and I still don't know what to do with them thank you so much sir
😂 right
lol ikr
Thank you, now i understand why most of visual demonstarations use the "find the area" as example
Ephesians 6:10-18 says, Finally, my brethren, be strong in the Lord, and in the power of his might. Put on the whole armour of God, that ye may be able to stand against the wiles of the devil. For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places. Wherefore take unto you the whole armour of God, that ye may be able to withstand in the evil day, and having done all, to stand. Stand therefore, having your loins girt about with truth, and having on the breastplate of righteousness; and your feet shod with the preparation of the gospel of peace; above all, taking the shield of faith, wherewith ye shall be able to quench all the fiery darts of the wicked. And take the helmet of salvation, and the sword of the Spirit, which is the word of God: praying always with all prayer and supplication in the Spirit, and watching thereunto with all perseverance and supplication for all saints. The bible is no old book. You have to really let Christ open your eyes; to see the world in shambles. Many people say it's a religion to lock up people in chains, and say it's a rule book.. why? Because people hate hearing the truth, it hurts their flesh, it's hurts their pride, it's exposes on what things have they done..people love this world so much, s*x, money, power, women, supercars.. things of this world. Still trying to find something that can fill that emptiness in your heart. You can't find that in this world.. only in Christ, the bible is no chains, it's a chainbreaker. Breaking your sins into pieces... Repent now, and turn back to the true Lord only.. God bless.
😊😊😊
I passed pre calculus and I’m getting myself ready for calculus 1. So excited!!!
@@Substantialstem800Good luck. Hope you'll do better than me.
I wished I took pre calculus before calculus 2 cause I failed now i got to review for the next semester
I am in calculus 2 with out knowing anything
Emphasize why Calculus is so awesome in one minute. The understanding part is hanging out somewhere else in a mysterious place. Math teachers aren't good at explaining math because they are too excited about being good at math to have to explain it to those who are not. It's an inverse proportional equation. What happens is that students who are bad at math only hate math until they become good at math. The one's that make it, end up loving math; the one's that don't continue to hate math. It's like a cult that once you join, you go: I see that now.. it's all so logical. But the one's that don't, continue the underground movement of hate against math. Very few, if any math geniuses understand why math is so hard to many people. They only seem to understand why it's so simple to them. The true genius understands both simultaneously. Good night.
Most people who are good at things naturally tend to not understand how others are unable to do them also. If you are naturally good at something you do not think about how you learned it. That applies to all things.
Sometimes, people are blessed to understand that others see or feel things completely different from themselves. They try to think how others are thinking and how they can guide them to being able themselves. Those people are rare.
same with tech (hardware/communications and programming/networking) teachers and classes. some of these teachers just zoom through the material and just marvel at how genius they are themselves but just leave most students behind.
funny that i learned one very important thing from my breakdancing buddy who is now a teacher at a college...but he told me this over 10 years ago before he was a teacher. "you dont truly understand something until you can EASILY teach it, and people get it". but then u can talk about it still on a higher level with people who are very experienced/educated.
Amazing teacher! Thanks!!👍👍👍
Thank you so much sir
Wow😮❤👏🙏💯
Thanks I knew nothing about calculus but after watching this a few times I actually tested out of having to take Cal 1! thanks
thank you for the help bro i was thinking of taking Calculus course but after seeing your video i understood the the whole course
😅😅
So basically breaking down a shape into smaller pieces again and again until it matches with the area of the shape then use the formula on each shapes that you broke down and you can add that up and get a accurate estimated area CALCULUS IN A NUTSHELL
That's the way it was explained to me in the 8th grade.
While it seems too easy just remember: integrate to find area under the curve. That x^2 might represent the weight of a cable. The integral, then, is total weight between two supports at 2 and 5.
Cables don't hang in the shape of parabolas. That is a common misconception that high school algebra textbooks give for "examples" of parabolas.
@@carultch i appreciate your precision... my errant though was just a crude example to give calculus credibility.... to reveal ita beauty.
@Prodigious147 thank you, I think. But, no, I'm not gpt. I vividly recall when I first learned how complicated problems like suspended cables could be easily calculated with calculus....
@Prodigious147 ok
@@josedanielsanchezvidal8936 I know what a catenary is.
this tutorial so good I learned the entirety of calculus in 1 minute
maybe not all of it actually no where close to all of it
I feel like there's more than enough space to write the rule
Integral of Xⁿ=(Xⁿ⁺¹)/(N+1) to get X³/3 to give beginners an easy win. If you're looking for ideas, your next short could calculate just how much space.
"An easy win"?
Sarcasm much?
@MrUndersolo Nah, not really, except for my comment about there being more than enough space to add the formula. There are no free rides in math, but it gets easier if you learn the basics of the game. That means anyone who wants to understand this video must understand basic algebra, but if you don't include that formula they won't have a chance.
thanks so much
Thanks for this succinct explanation.
Jokes.
I’m not particularly good at math but how did he end up with x^3/3?
integral of x²
Integral of x^n = (x^n+1)/(n+1)
@@nerd5865What is an "integral"??
Thank you 😊!❤ I have a upcoming competition and I needed to learn calculus in a month and because of you I got it in 1 minute 😭♥️
Hello sir thanks for teaching the concept…I want to know one thing is there a way the Area under the curve of a random graph meaning if we don’t have the function for it and it doesn’t follow any pattern either.
Thanks and Namaste 🙏
Fantastic! Calculus is Awesome!
Can you do a video that shows how the rules for integration and doing derivives is proven?
I’m in my sophomore year of high
School rn idk why but I just wanna learn calculus seems interesting ngl
I recommend the video by organic chemistry. I'm in Pre Calc right now and it gave me a nice look ahead into what things will be like next year
Racist.
@@Revelian1982 Nice joke, really appreciated that
I find it fascinating but I'm not doing this kind of maths at school
How do you go from x squared to x cubed over 3?
why is it exponential by 3?
Where did tge 3 come from
What dis do for me future?
Very interesting
My mind was blown when I saw formulas that I have to use while I’m in confusion
@22:57 I really like the shape of these glasses, they’re so cute and very statement. Where did you buy them?
Honestly, this isn’t that bad of an explanation
Then it is as bad I feared. I'm a moron.😢😆😆
Please explain why ie the mechanism of why your doing what you’re doing not just calc rules!!
Love the graphics --do you have practice exercises with your lectures to buy?
Where did the 3 comes from
Explaine why the integral equals x^3/3?
In a non condescending way, do you know how to derive a function?
@@orans_ nvm, got it. The derivative of x^3/3 is x^2. He just did it in reverse
How is x^2 ~ x^3?
@@orans_I don’t, can you explain it to me?
@@orans_what is a "function" and how do you derive it?
You can estimate the area:
x = 2->3 y = 4->9 av = (4+9)/2 = 6½
x = 3->4 y = 9->16 av = 12½
x = 4->5 y = 16->25 av = 20½
So the estimated area Ae = 6½+12½+20½ = 39½ not bad.
The estimate is obvious too high because of the curve of y = x² ... the real value of y(2½) = 25/4 = 6¼, not 6½
Now again with real values:
y(2½) = 6¼ y(3½) = 12¼ and y(4½) = 20¼
with a total estimated area Ae = 6¼+12¼+20¼ = 38.75
Getting closer to the real area.
Making more and smaller steps in x will result in better estimates. Using a computerprogramm or Excel sheet will do the trick without integration.
It takes 100 steps to get 39.000
yea but its so ez to do it normaly
@@BingeBaconShortz For this equation it is better to integrate the function. But with very complex equations estimating is really a good choice to find an answer close enough to the analytic answer.
Awesome 🎉
My favourite 🤸🥳💃💯
Thx
❤, thanks
My teacher tells me that if I forget to add ad a constant, baby yoda dies!
I still don’t understand how you got x^3\3 instead of x^2
Here's the step-by-step solution to find the antiderivative of x^2:
Given:
f(x) = x^2
Step 1: Apply the power rule for integration.
∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration and n ≠ -1.
In this case, n = 2, so:
∫x^2 dx = (x^(2+1))/(2+1) + C
Step 2: Simplify the expression.
∫x^2 dx = (x^3)/3 + C
thank you chat gpt
+1
Very simple in my old age 53. I am searching for my retired maths teacher .
How to find areas in irregular shaped objects aka estimate. Thats calculus in a nutshell.
How is Y = X^2?
When plotting the graph 📈 the value of Y is equal to X^2. So when X= 2 then Y=4.
Now I get it!
So why exactly are we multiplying the Xs 🤔 subtracting the x points ,dividing by 3, then dividing both sides both times the x points 🤨 and then subtracting them 🤔
Thats epic 😮
Question: why would we want to know the area of that little yellow part?
Ty
I understood most of it, but I dont get why or how you get :x to the power of 3 over 3.
How was the integral converted to get that answer?
Anti derivative
Add one to exponent and divide by the exponent amount after you add 1
(x^(n+1))/n+1 + C
C represents the constant of integration
So it's just integration and derivation?
I watched this just for fun to see what calculus would be like and I want to cry.
What is d and why did you get rid of it
Units?
tengkyu bang aku jadi albet ainstain aku fe
ns abang
3 semesters in the classroom and still don’t get it. Professor was generous with the C-. Should have failed me so I could get a do over in summer school.
bro what is the area of that yellow shaded part
Almost failed my quiz. Ty for this
Where did the 3 come from?
5-2 = 3 (the area has a width of 3)
Of course the answer is 39. How did I not know that? My brain started crying after the word “awesome.”
After having taught math for more than 20 years I have
As a sixth grader, I will learn and understand calculus probably in a month or less (Probably will take a while)
Love your high hopes and enthusiasm but it’s important to be realistic! If you put in the time, you can understand the basics in a month or so but to understand what’s truly happening, it’s important to grasp, geometry algebra, and trigonometry before you start your calculus journey! Best of luck in your math endeavours!
-An AP Calc B/C student
@@OgJail Yeah the basics! Also I'm doing 7th and 8th grade math
that's great! I hope you succeed! goodluckk
@@Real_DripBaconwhen i was in 5th i also started to solve maths of 9,10th now iam in 11th
Oh cool, I am also trying to learn calculus so I can use it for physics, I don't think that there are AP courses in my country. Otherwise I wouldn't learn it, because they do not teach it before really high levels of education in my country. Also I am 7th grade in my country which is 8th in USA lol.
I understand everything now
For the people who claim I should turn off my brain... this is how... my brain shut down within 4 seconds
Integration understood
great! now i understand how my dog feels when i talk to him LUL
Where did you get the 3? It seems to just appear. Is it the LW?
it's some rule you will learn, dw about it for now. you add one
you add one to the exponent x^2 + 1 = x^3.
the three you see is from 2 + 1. The 2 is the squared that's why it's 2
What about the unit?
@hiddentymesLegendary
…since this is an area problem he should point out that the square units must be included with the answer. In this case the units are arbitrary since none were specified. So each of us can choose to give whatever units each of us desires. Since we weren’t given any particular units, I could call mine square feet. You likewise may choose to call yours square meters… and on and on, for whatever units each of us chooses, since he didn’t specify any particular units.
Can we find the area of any curve which is not even a function?
@@hiddentymesLegendary
…far be it from me to speak ex cathedra, but to my scant understanding of the subject of calculus, the whole idea of integral calculus is integrating functions that are integrable, and differentiating functions that are differentiable. That is, a function must first be continuous, therefore discontinuity is a factor, their limit must exist, and other crucial factors, etc. Some, for reasons due to such factors must be integrated piecewise. So it seems, to me at least, that your question is somewhat self contradicting. I say that respectfully. But a curve, that is, a function must first have an equation in order for it to be differentiated or integrated.
Then at some places I saw that with calculus we can find the area of any curve . That means we can't find the area of every curve? Or any shapes bounded by curve?
@@hiddentymesLegendary
A curve must first be a function. A function must have an equation which can then be integrated or differentiated. Given any curve that meet those basic conditions and obey a few other restrictions then any of “those” curves can be integrated. Some equations, or functions, or curves, can’t be integrated or differentiated on some intervals of their graphs due to lack of continuity, or discontinuity, for example. Area under some curves have to be approximated by additional techniques in calculus. If I drew some random curve without fitting an equation to it, it couldn’t be integrated or differentiated. If we drew some random curve on a graph and bounded it from 0 to 3, say, but had no equation for that curve we couldn’t integrate or differentiate it. Equations for functions, or curves, can be built from data, but that’s beyond my ability to discuss at this point. So… yes, any and every function, or curve, using those terms interchangeably, that meets the requirements that enable us to differentiate or integrate it can be differentiated or integrated.
Literally this is not only explaining how calculus is so simple but why we even do it actually so simple. Why aren't we taught it like this? I think we taught it in like a way that's rushed to get as much information in but it's not even that much information to just say why we do it and just so easy
This 's only small part of integration 😇
~definite integral~Area region~
Definitely
i sometimes wonder is π calculus?
How do you find the area of something thats not a function? If i were to draw a random shape could you find the area using calculus?
One way you could do it, is with Simpson's rule. This is a method that gives more computational efficiency than the standard Riemann Sums they teach you, when laying the groundwork for understanding integrals, in the prologue to calculus.
Simpson's rule constructs parabolas among each group of three data points, so that it samples a representative position, slope, and curvature, of the shape, that then varies throughout the shape's domain. The formula for Simpson's rule is set up so that you don't even need to think about parabolas to use it. This is what you'd do if you were given a shape and could measure data points to figure out what the curve is, but didn't know what mathematical function defined those points. One place you might see this, is the way CAD software estimates the volume of exotically shaped parts.
@@carultch ooo 😯
where’s three come from
5-2
That is because the antiderivative of a function x^n will be (x^n+1)/n+1
Math explanations always assume you know a certain level of math and I always get caught up on little unexplained parts. I can’t learn from an explanation if I don’t know where numbers are coming from.
How did Sir Isaac Newton (?) derive all the rules of integration? (Now THAT's utter genius!) There are hundreds of them and many are quite complex
I don't understand how people find calculus difficult, it's easier than algebra, (I barely passed that) 😂
How is it easier? I feel like algebra is the easiest.
@@RoyHoy nah-??????
I guess it's easier cause you're smarter lmao
depends on curriculum
@@RoyHoy wait till bro sees group theory
galois theory
abstract algebra
I GO SHOW MY FRIENDS
I’m learning this in math class and I’m in the sixth grade 😭😭
What the flipper doodles is that 1st symbol on A=__x2 dx
…and how did it get to x3!?
I get the division part because it’s automatically multiplication..im just lost
The funky S-shaped symbol is an elongated S called an integral sign. It means a continuous sum. The dx refers to a dinky change in x, that is infinitesimally thin.
The way that x^2 turned into x^3, comes from the power rule. In general, when you do the reverse process called differentiation, an expression in the form of k*x^n, turns into n*k*x^(n - 1). In other words, you leave the original coefficient (k) alone, and have the existing exponent (n) join the coefficient. Then you reduce the exponent by 1, so that it is now (n - 1). There are limit proofs of this rule you can look up, but in general, it comes from the binomial theorem of expanding (x - h)^n to show this from first principles of how we define the derivative.
To reverse this process for integration (which the fundamental theorem of Calculus proves is connected to derivatives) we reverse the formula, and get k/(n + 1) * x^(n + 1). So leave the coefficient alone, increase the exponent, and have the new exponent join the coefficient down below. Do this for x^2, and we end up with 1/3*x^3. Plus an arbitrary constant if applicable, as we do for unbounded integrals in general.
Basically calculus in all about the tangent line. As you might have remembered from Algebra 1 it uses a more complex version of the point slope form quotient which becomes the secant quotient and then the tangent quotient to find the limit and then this becomes the deifference quotient and this gives you the derivitive and its opposite cousin the integral. Then there is the shortened version of the difference quotient dx/dy and the rest in a lot of algebraic manipulation. I took it one time and failed miserably but what I didn’t realize is how much I learned in the process of failure. I have been going over the material again before I retake it and have found that my real problem wasn’t the calculus part of the course it was my failure to intuitively understand college algebra and trig. It’s so cool that if you fail it you might be in love with its complexity like me and be ready to retake it. One thing that makes it cool is the incredible applications of calculus which include space travel. That might get you hooked so Google it and then you can find you are doing simpler but the same basic math they used at NASA to put a man on the moon and the pathfinder on Mars. What kind of smack can you talk about that!
Why would I want to understand things that would result in being employed as a tool , day in day out?
How ia it 39 i only got 21 ???
instructions unclear, i am now calculus.😊
ok i’m ready to be an astrophysicist
Dang we just completely skipped limits and derivatives and went straight to integrals 💀
12:23 Dora temper tantrum😂
Honestly calculus is easier than Algebra
🤨🤨🤨🤨🤨
Trippen
no it's not
Is everything OK at home?
@@lapikolko2😂😂😂😂
Yeah, I was thinking about the last episode of friends while I watch this……
COOL 😎
Where the hell the 3 come from?
39 what?
Anyone help me calculus
Bruh the slope?
1/4 of the circle area.
Take a square area.
And then subtract it.
Chat please tell me I’m not the only one who can do calculus and in 6th grade
As an eigth grader i can easily solve it i love maths
here's a problem
find all positive integers n such that
n!+1 is divisible by n+1
Suuuuu asam
The only "dx" that I know is "D-Generation X"! 😅
Sir, you have only covered like 0.1% of the very basics in one of many branches of calculus.
Why is calculus easier than allgebra for me.
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