I was always bad in school. Was terrible at math. Barely got my diploma. In my mid 20s now and I study physics just for fun. Been having learning walls and knew I had to start here. I honestly cried at the end of this video. I could see the math visually and Understood it’s application so well. Never thought I’d see math in this way. Thank you so much. All the time I wasted in school. Feels terrible.
any advice ? im bad at math and the highest math for me is geometry in my sophomore year and im graduating highschool early. and im doing cal 1 and cal 2 in college next month
At school I had terrible math teachers that put me off the subject for life. This did not stop me becoming a computer programmer for over 40 years. In all that time I never needed calculus, and only used algebraic equations a few times. Neverthless, your videos are good and will be useful for people that have to learn this subject.
You don’t really need calculus to become a software developer but you do need good logic plus the ability to copy and paste. Not forgetting AI code generators 🤔
This was a very good explanation for 72 year old guy who flunked calculus in college once. You mentioned note taking. Note taking is incredibly difficult. If the student had a piece of paper in front of them showing the drawings and the formulas you presented it might be easier.
Great tutorial really sooths some of the initial intimidation of complex math. considering that I am a 14-year-old boy who can't even focus on basic pre-algebra it is miraculous that this video actually made vauge sense to me and kept my attention for 20 minutes. this is one of the best math videos i have ever seen
I loved algebra in school and peaked there in math, because without understanding pre-calc it wasn't fun or easy anymore. I know I'm smart enough for it, but I wanted to learn other things. I graduated with an arts degree 10 years ago, and have been doing some deep soul-searching about going back to school to embark on a new career. This has led me to consider civil engineering as something I've always been passionate about, but the math terrifies me! I enrolled in some coursera classes to see how challenging it would be and gauge my learning deficit, but this video has made me feel SO much better about pursuing this! Thank you!
Thanks. I had no idea what I was trying to learn in Calculus and switched majors. I’m 75 , started tryin to refresh my algebra & found it’s kinda fun. BTW my major was in graphic design
Thank you for the video. Please do not stop and continue to create more in depth Calculus videos, and yes Calculus is a very fascinating subject or may be language. Love it.
The first calculus class I took was one I dropped, because the professor hated tech so much, while a lot of my learning methods are tech heavy. This video did NOT disappoint in reinvigorating me to push my math skills to the max and be the game designer I've always dreamed of being.
for anyone wondering, dx it essentially indicates the infinitesimally small change in x that is being summed over as part of the integration process. Without dx, the integral would lack the necessary information about which variable is being integrated. or atleast whatever that means
Thanks I am horrible at math and I was looking into majoring in meteorology later on and becoming a storm chaser, and apparently it involves calculus and physics I'm starting to really learn this a little earlier (I'm starting high school in two months) because I've heard the earlier you pick up the skills needed for meteorology, the better
This was very well explained and I plan on taking this course. I had 2 horrible professors that made Data Management so unnecessarily difficult and they talked way too much about irrelevant things. Thank you so much and don’t worry about your voice!
That was an interesting re-introduction to calculus. I haven't used it since my engineering college days over 50 years ago and I dislike forgetting something I liked using in the past. So now onto the next stage and to work though some more examples.
I appreciate that you took the time to create this video. I wish you had a versions of your explanation that stayed succinctly and absolutely on track with solving the problem in as few words as possible, leaving out all the extra verbosity 8:25 Maybe I'm not your target audience but I'd appreciate the availability of the speed course as a refresher. I took calculus in college back in '85 .
I started smiling 🙂 I believe I'm going to understand this lesson, The introduction is an interpretation of my mind 😢😂❤❤❤. Ive been looking for this kind of video, God bless you🫶🏽👏🏽.
I barely got past fractions in school. I actually was able to understand this and love the applications of finding area and volume for all sorts of shapes. Thank you sir.
Thanks for the great videos. I’ve recently been self studying calculus. The books I’ve read explain how to solve calculus problems, but never showed how it applies to a graph with real numbers, step by step. Your videos have helped me conceptually understand what I’m doing when solving problems
Thank you. ... Now, I am going to have to sit down and take some really clear notes so that I can fully understand the quirky steps needed to solve these kinds of problems. 👍
God bless u. I haven’t took calc. I will probably take it next semester or next year but I need to take the managerial calc. Idk if it’s because it’s almost 4:AM on a Thursday morning. But I understand this. Thank u I hope this is what calc looks like and doesn’t change for the love of god.
This exemplifies the failure of the public school system, which rushes through the explanation and then piles on the homework. If the explanation doesn't click with you immediately, then you're out of luck. I am severely jealous of kids in the modern era, who have grown up with the Internet. I can only imagine what I could have accomplished with it during the 70's through the 90's. Sadly, since today's kids have never known life without the Internet, they don't understand what they have. It really is true that youth is wasted on the young.
Cool I am in 7th grade and haven't finished pre algebra yet and made 100% sense to me. I will take pre calculus in high school. It reminds me of slope of a line.
When I was younger I was far more right brained and HATED all math 😂 But ironically now that I’m a lot older I’m starting to naturally learn and understand math, idk what da hells going on with me lately, but I’m here for it! 😂
Good explanation. Maybe a little too fast for an absolute beginner, but, they can always watch it several times over (perhaps inserting their own values) and write it out on paper. This will be more beneficial than using a calculator I feel......To make the 'Parabola' more visual, perhaps put a link in to show the various conic sections ?
I just started my Masters degree and it includes calculus. Thank you for these videos and hope your channel grows. btw subscribed today and cant want to learn more
I am actually a 7 th grader very interested in math ( actually idk why iam learning this in this age but 😅) . You teach very well 👏 l ,thankyou for your notes! 📝 😊
Hello John: I enjoy your videos very much. I was born and educated in an English Grammar School back in the mid fifties to early sixties (yes I am ancient and left school in 1961). I find it puzzling when you mention students taking cell phones to class ???. We were not allowed to take a calculator to class !!! Had we taken one to an exam room, we would have been disqualified. The only thing we were allowed to carry was a slim book of log tables. All calculations were made by hand. English kids were made to know multiplication tables just like learning A.B.C.s at a very young age. Does England sound very Dickensian to you John?
I think it was very well explained, at least to a 72-year-old who flunked calculus once in college and got a D the second time around. You did mention note taking. This is incredibly difficult for a young student or an old guy. As far as I know there is real no class on note taking. Now if the students had a handout on paper in front of them where they could kind of write little notes that might be of some use. I also think that is very important to give students a real life use of why you would ever want to do a calculation like you should. Something like when SpaceX launches the first the rocket. X could be the pressure building up on the rocket as it approaches Max Q
A nit: proBlem not prolem. It's a very small nit. (30 years since I taught my last algebra class. 60 years since calculus. I still remember some. You are helping me slow cognitive decline. Thanks)
The 1>2 area is an approximate triangle. Why not figure the area of the triangle on each side, then subtract to figure the areas on each side of the curve?
I love your way of presenting math. Its super cool. Do you do slightly more advanced courses? Lagrangians, Fourier and Laplace transforms, Hamiltonian Operators, tensors, matrix mechanics?
Which definite integral of n = 3 to n = 1 are you referring to? And it should be n = 1 to n = 3, not n = 3 to n = 1. That would give a negative answer and there no such thing as a negative amount of area, land, for instance! Area can be subtracted from another area, but in the case of a single area, such as here, there’s no such thing as negative area, or negative length, or negative time, etc. Those things do exist! It’s an existential truth ..can’t have -88 square acres of land …there is no such thing….?! If you mean this same parabola here, you’d simply do the same thing he does here with 0 to 2, or, as you say, n = 0 to n = 2 (these are called the “limits of integration,” 0 and 1 being the lower limits, and 2 and 3 being the upper limits), respectively; but for the “limits of integration” which you mention here, n = 1 to n = 3, you’d plug in 3 and 1 for x instead of plugging in 2 and 0 for x in the integral (x^3/3) - (x^3/3): (3^3/3) - (1^3/3) = (27/3) - (1/3) ≈ 9.000 - 0.333 ≈ 8.667 square units. Units being whatever is specified: feet, yards, meters, inches, etc. Here, nothing’s specified, so we use the most general term, square “units.”
As I'm new to Calculus I'm also new as to how to write about it. However, I can assure you that calculating a negative area can have a use. Up/down, right/left, matter/anti-matter.... LOL
@@tonymanns8249 My intent is not to say that we can’t subtract some particular amount of area from another, of course we can. Subtract 5 acres from 10 leaves 5 acres. So that it’s a mathematical as well as a real life possibility. The land exists. But, that’s just it, the land we subtract is real, it exists, it has to! In that sense, mathematically, it has a negative number, but the land itself exists.
I don't understand how they came up with this formula as bein the formula for the area under the parabola/line? I can accept it as being so but by what reasoning did they derive the formula???
@ Robert Fanfalone Geometrical argument and analysis in trying to find the areas of odd shapes that have no equations but are built through geometrical analysis and scientific investigation and observation that began with the Greeks, especially with Archimedes, who lived around 287-212 B.C. A brief research of the topic of “The Quadrature of Parabola” of Archimedes will give you some insight and mental grasp into how the formula came about centuries ago with Archimedes’ discovery and development of the formula x^3/3 + C through his work by way of geometrical analysis of the quadrature problem. And it is said that had Archimedes known the things learn in the later centuries he would’ve discovered the calculus… way back then! Geometry, algebra, geometrical analysis, trigonometry, to name a few, and of course scientific investigation all serve as the origin and foundation not only calculus, but also functions as the one seen here. This stuff goes way back for centuries. There’s a scientific video series by Cal State titled “The Mechanical Universe and Beyond” which debuted around 1985 or so. And it’s done in a most wonderful narrative form as the narrator goes through the history of the sciences and mathematics from the earliest recorded time in history up to the mid to late 1980’s! It has 56 episodes of roughly 30 minutes each! Check it out here on RUclips! It gives you the history of all mathematics, all the sciences and brief biographies of all the great mathematicians and scientists, especially, it’s narrates the history of the efforts of proclaimed inventors of the calculus, Newton and Liebnitz, and the little spat and beef over the race between them to be the first to invent the calculus, interesting, it narrates the discovery of “The Law of Falling Bodies” which maps out the path of a parabola and discovered by Galileo, as well as his life trials and other discoveries, a genius he was, as well as the others, but he’s one of my favorites, if not my favorite… sometimes it’s Newton, though. And it gives you both the origin and the process of developing mathematical functions, and the likes. And to top things off, it teaches calculus and physics as you go through the entire series! Incomparably valuable resource… don’t miss it! And you’ll never regret it!
![BLACK BAG - Official Trailer [HD] - Only in Theaters March 14](http://i.ytimg.com/vi/Du0Xp8WX_7I/mqdefault.jpg)
I was always bad in school. Was terrible at math. Barely got my diploma. In my mid 20s now and I study physics just for fun. Been having learning walls and knew I had to start here. I honestly cried at the end of this video. I could see the math visually and Understood it’s application so well. Never thought I’d see math in this way. Thank you so much. All the time I wasted in school. Feels terrible.
any advice ? im bad at math and the highest math for me is geometry in my sophomore year and im graduating highschool early. and im doing cal 1 and cal 2 in college next month
@@josem-wx7uz your Math skills are undeveloped for Calc.
@@plozar Yeah i started taking college algebra and i take trig next
YOUR PAST NEVER EQUALS YOUR FUTURE.....GOOD OR BAD. Keep breaking down the walls.
Thank you very much.
At school I had terrible math teachers that put me off the subject for life. This did not stop me becoming a computer programmer for over 40 years. In all that time I never needed calculus, and only used algebraic equations a few times. Neverthless, your videos are good and will be useful for people that have to learn this subject.
Could you tell me what GCSE’s you did for this (if you live in the uk) and a levels for computer programmer cause I will not be doing calculus no way
You don’t really need calculus to become a software developer but you do need good logic plus the ability to copy and paste. Not forgetting AI code generators 🤔
Teaching starts at 5:48
Quite helpful 😢
Actually, 5:30;
This was a very good explanation for 72 year old guy who flunked calculus in college once. You mentioned note taking. Note taking is incredibly difficult. If the student had a piece of paper in front of them showing the drawings and the formulas you presented it might be easier.
🙏
Note taking takes a lot of self discipline and skill
I'm 72, and i flunked College calculus 'cause i ran a Surf shop at the same time and found surfing more fun than math...
Southern Cal??
I’m 76 and found this explanation great, except what C was
Great tutorial really sooths some of the initial intimidation of complex math. considering that I am a 14-year-old boy who can't even focus on basic pre-algebra it is miraculous that this video actually made vauge sense to me and kept my attention for 20 minutes. this is one of the best math videos i have ever seen
A very brilliant math student once told me that if you want to learn something..teach it...😅
I loved algebra in school and peaked there in math, because without understanding pre-calc it wasn't fun or easy anymore. I know I'm smart enough for it, but I wanted to learn other things. I graduated with an arts degree 10 years ago, and have been doing some deep soul-searching about going back to school to embark on a new career. This has led me to consider civil engineering as something I've always been passionate about, but the math terrifies me! I enrolled in some coursera classes to see how challenging it would be and gauge my learning deficit, but this video has made me feel SO much better about pursuing this! Thank you!
Thanks. I had no idea what I was trying to learn in Calculus and switched majors. I’m 75 , started tryin to refresh my algebra & found it’s kinda fun. BTW my major was in graphic design
It is said that working math problems may keep our brains in great condition in senior years.😊
You discourage me, I'm 79 . Can't dispense with maths lessons. Have just learnt matrix and now want to proceed with Calculus but you discourage me
Thank you for the video. Please do not stop and continue to create more in depth Calculus videos, and yes Calculus is a very fascinating subject or may be language. Love it.
totally agree
Mathematics is a language😊
Fr
This will help me learn a lot more in school and get me to be an aeronautica engineer. Thank you so much, TabletClass Math.
The first calculus class I took was one I dropped, because the professor hated tech so much, while a lot of my learning methods are tech heavy. This video did NOT disappoint in reinvigorating me to push my math skills to the max and be the game designer I've always dreamed of being.
Very good. Most people that teach calculus don’t explain what you are really doing well enough.
I'm just a man in his early 40s learning a new skill for fun. Thank you for taking the time to make it possible for me to do so. Love this stuff
for anyone wondering, dx it essentially indicates the infinitesimally small change in x that is being summed over as part of the integration process. Without dx, the integral would lack the necessary information about which variable is being integrated. or atleast whatever that means
I struggled through many calc classes in college. Imagine if I had RUclips to help, what a difference that would have made!
Thanks I am horrible at math and I was looking into majoring in meteorology later on and becoming a storm chaser, and apparently it involves calculus and physics
I'm starting to really learn this a little earlier (I'm starting high school in two months) because I've heard the earlier you pick up the skills needed for meteorology, the better
This was very well explained and I plan on taking this course. I had 2 horrible professors that made Data Management so unnecessarily difficult and they talked way too much about irrelevant things.
Thank you so much and don’t worry about your voice!
That was an interesting re-introduction to calculus. I haven't used it since my engineering college days over 50 years ago and I dislike forgetting something I liked using in the past. So now onto the next stage and to work though some more examples.
I appreciate that you took the time to create this video. I wish you had a versions of your explanation that stayed succinctly and absolutely on track with solving the problem in as few words as possible, leaving out all the extra verbosity 8:25 Maybe I'm not your target audience but I'd appreciate the availability of the speed course as a refresher. I took calculus in college back in '85 .
I started smiling 🙂
I believe I'm going to understand this lesson,
The introduction is an interpretation of my mind 😢😂❤❤❤.
Ive been looking for this kind of video, God bless you🫶🏽👏🏽.
God bless you as well 😁💗
Thank you.
I came to refresh my memory.
Excellent introduction to a seemingly-daunting topic. Thank you so much! I definitely feel more comfortable about calculus.
I barely got past fractions in school. I actually was able to understand this and love the applications of finding area and volume for all sorts of shapes. Thank you sir.
5:45 it really starts around here
Thank you! I'm beyond exasperated with the ridiculous blather! Maybe I'll hang on a bit.
Thank you!!! I understand why the intro was there, but that intro wasn't for me.
Thanks for the great videos. I’ve recently been self studying calculus. The books I’ve read explain how to solve calculus problems, but never showed how it applies to a graph with real numbers, step by step. Your videos have helped me conceptually understand what I’m doing when solving problems
Thank you. ... Now, I am going to have to sit down and take some really clear notes so that I can fully understand the quirky steps needed to solve these kinds of problems. 👍
I graduated from GED in 1993 studied a calculus equation disk's and washers memorized the entire equation and I completely understand it.
i love math and am very critical of how people teach it to me but you explain it very well thank you
God bless u. I haven’t took calc. I will probably take it next semester or next year but I need to take the managerial calc. Idk if it’s because it’s almost 4:AM on a Thursday morning. But I understand this. Thank u I hope this is what calc looks like and doesn’t change for the love of god.
imagine 22mins video explain in details what ur teacher or lecture don't even do in the entire session 💯🙌
This exemplifies the failure of the public school system, which rushes through the explanation and then piles on the homework. If the explanation doesn't click with you immediately, then you're out of luck. I am severely jealous of kids in the modern era, who have grown up with the Internet. I can only imagine what I could have accomplished with it during the 70's through the 90's. Sadly, since today's kids have never known life without the Internet, they don't understand what they have.
It really is true that youth is wasted on the young.
Calculus AB is being taught to juniors in high school. So help is needed.
Great lesson! Im a year 10 and this was very clear and knowledgable
Cool I am in 7th grade and haven't finished pre algebra yet and made 100% sense to me. I will take pre calculus in high school. It reminds me of slope of a line.
Good information! I love the detail - you explain the detail and assume we need explanations which is true for me.
this was soi incredibly helpful, thank you so much!!!
You have skills to make it simple! Bravo
When I was younger I was far more right brained and HATED all math 😂
But ironically now that I’m a lot older I’m starting to naturally learn and understand math, idk what da hells going on with me lately, but I’m here for it! 😂
Thank you, I understood everything except for the dx and the +c at the end
yea i had to do my own reserch for that one
Good explanation. Maybe a little too fast for an absolute beginner, but, they can always watch it several times over (perhaps inserting their own values) and write it out on paper. This will be more beneficial than using a calculator I feel......To make the 'Parabola' more visual, perhaps put a link in to show the various conic sections ?
thanks i was looking for a explaination about calculus, i was serching for something like this.
I just started my Masters degree and it includes calculus. Thank you for these videos and hope your channel grows. btw subscribed today and cant want to learn more
Wonderful explaination. RUclips is getting me the most needed videos in recommendation.
I’m in year 10 and 14 calculus is really really fascinating and interesting to me and you explained it very well thank you
Thank you for the introduction to Easy Calculus!
Extremely useful but how you get the algorithm for it?
Thank you so much! Very well explanation for a beginner.
I am actually a 7 th grader very interested in math ( actually idk why iam learning this in this age but 😅) . You teach very well 👏 l ,thankyou for your notes! 📝 😊
Awesome video! At the end it starting making sense for me!
This was really helpful. Thanks Prof.
Great review for me. Thanks much.
Wow, you actually did your job. Taking precalculus.
This is fantastic, I really love it.
YES! This is one of the best match courses/classes ever, thank you!!
Great teaching, thank you!
I'm teaching myself for fun and this is a great reintroduction
Thank you.
Skip the intro /commercial (25% of video) and go to 5:40.
Hello John: I enjoy your videos very much. I was born and educated in an English Grammar School back in the mid fifties to early sixties (yes I am ancient and left school in 1961). I find it puzzling when you mention
students taking cell phones to class ???. We were not allowed to take a calculator to class !!! Had we taken
one to an exam room, we would have been disqualified. The only thing we were allowed to carry was a slim
book of log tables. All calculations were made by hand. English kids were made to know multiplication tables
just like learning A.B.C.s at a very young age. Does England sound very Dickensian to you John?
Thank you for making these videos it really helps dimestifyimg the subject.
Yes, you did a decent job! Thanks
Is was indeed a decent job. Tyvm Sir
Sweet …thanks Professor
Wow, you did a great job. I'm really impressed by the clarity.
Amazing introduction to Calculus. Thanks, man.
I think it was very well explained, at least to a 72-year-old who flunked calculus once in college and got a D the second time around.
You did mention note taking. This is incredibly difficult for a young student or an old guy.
As far as I know there is real no class on note taking.
Now if the students had a handout on paper in front of them where they could kind of write little notes that might be of some use.
I also think that is very important to give students a real life use of why you would ever want to do a calculation like you should.
Something like when SpaceX launches the first the rocket. X could be the pressure building up on the rocket as it approaches Max Q
I agree that note-taking is hard in math. Maybe some handouts with mini-quizzes built into them.
Simple way of explaining maths.good job.
Video starts at 5:46.
Such a big help for slow learner like me ty so much and godbless
Nice workframe that you created teaching Math. Got a lot of insights. Abou maths
A big thank you 😊. Thank you very much.
well explained thank you...
Maybe I missed something here, but why did you plug a 2 in for the value of 'n' in the first equation? why not use 3 or 4 or anything else?
Specifically looking to solve the x squared(^2) function, see 10:06 into video
A nit: proBlem not prolem. It's a very small nit. (30 years since I taught my last algebra class. 60 years since calculus. I still remember some. You are helping me slow cognitive decline. Thanks)
Great Explanation Skills!!!
nice job very well explained Thank You So Much
Pretty cool man! Thanks 🙏🏽
I’m 12 but really good at this stuff
Same
The 1>2 area is an approximate triangle. Why not figure the area of the triangle on each side, then subtract to figure the areas on each side of the curve?
Which application are you using for this Green board, pens, and colors?
Such a great lead. Calculus demystified
Good video 🙌
I love your way of presenting math. Its super cool. Do you do slightly more advanced courses? Lagrangians, Fourier and Laplace transforms, Hamiltonian Operators, tensors, matrix mechanics?
are u with us 😂😂 or in the Pluto planent😂
Lol, sounds like you don’t need help.
The fact I can’t even tell if you’re speaking English or not says a lot 😭 lagrangians what now?
hello i am in grade 6th i am getting bored of all the easy classes so i wanted to stduy calculas perfect video
When are you dropping pre calculus on your website?
It is wonderful, enriches understanding
guys is it always x*2 or does it change?
Excuse me but if I may ask if you do anything with the "dx" part
Go search for other calculus videos
Or search it up
This guy cares more about yapping than the actual lesson 😭
My first ever calculus lesson. OH BOY !
Thanks for everything 😊
Thank you soo much. ❤❤❤
Im in grade 8 im looking for a boost and your explanations help me a lot
Thanks!! Excellent explanation!
Helpful Math videos. Nice to have an easy tutorial
Where does x come from?
Nice intro for use who are new to Calculus. I wish he would have given the answer for the definite integral of n=3 to n=1.
Which definite integral of n = 3 to n = 1 are you referring to? And it should be n = 1 to n = 3, not n = 3 to n = 1. That would give a negative answer and there no such thing as a negative amount of area, land, for instance! Area can be subtracted from another area, but in the case of a single area, such as here, there’s no such thing as negative area, or negative length, or negative time, etc. Those things do exist! It’s an existential truth ..can’t have -88 square acres of land …there is no such thing….?! If you mean this same parabola here, you’d simply do the same thing he does here with 0 to 2, or, as you say, n = 0 to n = 2 (these are called the “limits of integration,” 0 and 1 being the lower limits, and 2 and 3 being the upper limits), respectively; but for the “limits of integration” which you mention here, n = 1 to n = 3, you’d plug in 3 and 1 for x instead of plugging in 2 and 0 for x in the integral (x^3/3) - (x^3/3): (3^3/3) - (1^3/3) = (27/3) - (1/3) ≈ 9.000 - 0.333 ≈ 8.667 square units. Units being whatever is specified: feet, yards, meters, inches, etc. Here, nothing’s specified, so we use the most general term, square “units.”
As I'm new to Calculus I'm also new as to how to write about it. However, I can assure you that calculating a negative area can have a use. Up/down, right/left, matter/anti-matter.... LOL
@@tonymanns8249
My intent is not to say that we can’t subtract some particular amount of area from another, of course we can. Subtract 5 acres from 10 leaves 5 acres. So that it’s a mathematical as well as a real life possibility. The land exists. But, that’s just it, the land we subtract is real, it exists, it has to! In that sense, mathematically, it has a negative number, but the land itself exists.
Thanks for the video.
Very good explanation for 79 years old woman
It have seen self explanatory, but does takes a lot of practicing to get the hang of it
Makes me want to watch Good Will Hunting!
Good explanation
I don't understand how they came up with this formula as bein the formula for the area under the parabola/line? I can accept it as being so but by what reasoning did they derive the formula???
@ Robert Fanfalone
Geometrical argument and analysis in trying to find the areas of odd shapes that have no equations but are built through geometrical analysis and scientific investigation and observation that began with the Greeks, especially with Archimedes, who lived around 287-212 B.C. A brief research of the topic of “The Quadrature of Parabola” of Archimedes will give you some insight and mental grasp into how the formula came about centuries ago with Archimedes’ discovery and development of the formula x^3/3 + C through his work by way of geometrical analysis of the quadrature problem. And it is said that had Archimedes known the things learn in the later centuries he would’ve discovered the calculus… way back then! Geometry, algebra, geometrical analysis, trigonometry, to name a few, and of course scientific investigation all serve as the origin and foundation not only calculus, but also functions as the one seen here. This stuff goes way back for centuries. There’s a scientific video series by Cal State titled “The Mechanical Universe and Beyond” which debuted around 1985 or so. And it’s done in a most wonderful narrative form as the narrator goes through the history of the sciences and mathematics from the earliest recorded time in history up to the mid to late 1980’s! It has 56 episodes of roughly 30 minutes each! Check it out here on RUclips! It gives you the history of all mathematics, all the sciences and brief biographies of all the great mathematicians and scientists, especially, it’s narrates the history of the efforts of proclaimed inventors of the calculus, Newton and Liebnitz, and the little spat and beef over the race between them to be the first to invent the calculus, interesting, it narrates the discovery of “The Law of Falling Bodies” which maps out the path of a parabola and discovered by Galileo, as well as his life trials and other discoveries, a genius he was, as well as the others, but he’s one of my favorites, if not my favorite… sometimes it’s Newton, though. And it gives you both the origin and the process of developing mathematical functions, and the likes. And to top things off, it teaches calculus and physics as you go through the entire series! Incomparably valuable resource… don’t miss it! And you’ll never regret it!
@@ndailorw5079
Great info Robert! Thank you for sharing the details.