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!

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

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

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.

Then it is as bad I feared. I'm a moron.😢😆😆

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.

integral of x²

Integral of x^n = (x^n+1)/(n+1)

That's the way it was explained to me in the 8th grade.

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

Jokes.

~definite integral~Area region~

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

It takes 100 steps to get 39.000

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?

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.

5-2 = 3 (the area has a width of 3)

🤨🤨🤨🤨🤨

Trippen

Calculus is analytical geometry Trig Algebra and arithmetic doe… But find an area under a curve with the fundemental theorem of calculus is soothing… All you need to know is how to define your bounds of integration integrate and evaluate You can use first principles or FTC.

no it's not

Is everything OK at home?

5-2

That is because the antiderivative of a function x^n will be (x^n+1)/n+1

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

When plotting the graph 📈 the value of Y is equal to X^2. So when X= 2 then Y=4.

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 😯

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.

here's a problem find all positive integers n such that n!+1 is divisible by n+1

your future :)

Fun times ahead. You kids now a days have so many resources online. Easier to rewatch these short videos as much as you want to learn rather than books that can seem confusing. Ability to learn got a whole lot easier. Just stop watching so many cat videos.

im also in 7th grade, i understand this cuz im a math nerd (kinda)

Don't feel bad, I took college algebra and I haven't the faintest idea what he said! 😂

I recommend reading about calc if you want to understand it

@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.