What is Integration? Finding the Area Under a Curve
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- čas přidán 16. 07. 2024
- Ok, we've wrapped up differential calculus, so it's time to tackle integral calculus! It's definitely the trickier of the two, but don't worry, it's nothing you can't handle! First things first, what is integration? Well it's that thing we mentioned way back in the introduction clip, when we talked about adding up the infinite tiny rectangles. Just watch and you'll see!
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Dear Professor Dave, you explained integration to me in just under nine minutes. WOW. Thanks, Professor Dave. I am now your happiest patron!
thanks for your support!
@@ProfessorDaveExplains please explain about you
Thank You professor Jesus
Lol 😂😂
lol.
Yeah.... Coz he's the school messiah for last minute study.... Lol 😅
Matnematics is the status of the world to have his own life experience as a good place to students and to be the best way to do this in the future of your business and how you can get the most important information to make your business is not the only ones that can who you want to do for the I know that you are so cDvlD and you are not the only ones that can who you want to do for the cDvlD of your life in the world of music and the world to have his own life experience
Amen to that
As a programmer who didn't learn calculus, integrations or anything else like that, this is GOLD. Thank you!
Nice, this is way better than binge watching Netflix.
Then, after watching this, try to watch 3Brown1Brown. It is nice to complement this video to the videos of 3Blue1Brown.
Rinkazhi Rinkashime Lol of course, his videos give a much deeper conceptual understanding of the subject matter. However, the procedure itself is covered more in Professor Dave’s videos.
You have said it. I watch video tutorials more than watching TV.
@@pinklady7184 You still watch TV!?
930 8323 Very rarely. I haven't watched TV in many months. After work, I usually go straight to bed and watch tutorials on tablet or read ebooks at Open Library. Just yesterday, my sister bought a large TV screen and installed it in our home. The new TV is ENORMOUS and screen resolutions is high. It comes with wifi. Last night, I was watching Blender tutorials (3D modelling) on CZcams, all on TV screen.
The thumbnails of drama and documentaries on TV look VERY ENTICING and TEMPTING. I resisted temptations.
You are literally my Calc II teacher right now thanks to distance learning lol so THANK YOU!! This was very helpful!! We need content like this now more than ever.
My teacher never taught me all that when I was at school...When I watched a video related to entropy , I got scared by the integral sign just like the way I got when I was back in high school. I work as an automation engineer in food and pharma sector and have watched some of your nice videos related to pharma industry. Now I have got the clearer idea of why integration is important and hoping to make use of the knowledge in future. Now I also realize how bad the situation was for us before these videos become available. Professor Dave inspires me to face my old high school and college demons and win the fights I lost back then. Teachers like you provide us with an opportunity to fix the gaps we had in our early education and provide us confidence to upgrade our brains for the future....Great Video and wishing the best for you and your channel😃
Your videos are explained so well! Thank you! The time put into these animations really reflects the viewers ability to understand it as well! Keep it up!
Also this unit is actually pretty interesting. I never thought I would hear myself say math is interesting but seeing how calculus finally folds out is kinda cool.
An excellent simple well illustrated explanation. Thank you very much.
Thank you very much for your effort in explaining these hard topics, really appreciated
Thank you for explaining how to identify the part of the equation that identifies the height of the rectangle and the part that identifies the base. I will not move on to fourier transforms until calculus makes sense to me. I think I need to work on a few examples to let it sink in.
Wow, this really helped me to understand. Thank you very much!
Superb explanation...it's crystal clear...Thank you so much Professor Dave!!
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Hey Dave, my teacher taught us about left hand rule, right hand rule and midpoint rule, how do you implement them into the summation formula (Riemann sum)?
Thank you so much for the Calculus videos, Professor Dave! I'm about to take a CLEP exam for Calc. and the study videos I originally used (by Modern States) were no help at all. More people need to know about you!
I very much appreciate the work you've put into your series of vids. But, the problem is that no one explains why calculus was invented, why it works with physics, what the area of an integral is suppose to physically mean, on and on. As a guy with a BS Physics, not one professor, nor textbook, ever bothered to explain/lecture the 'why' of math, which meant, that for many years, we were doing things by simple memorization.
What I learned is that the most important math concept is that of the pure number. Derivatives and integrals are pure numbers, as are fractions, ratios, percentages, geometry, trig, slopes, thermo entropy, and a bunch of other things. In other words, we were introduced to the overarching concept of all calculus back in the third grade, but no one bothered to explain its importance. I wish STEM vids would begin teaching the fundamental concepts of their disciplines prior to doing problems, that way the subject matter would be far more engaging...
Check out my tutorial introducing calculus. It’s the first in my calculus playlist. I teach precisely what you’re asking for.
Absolutely! That’s honestly the worst part about math, that nobody explains why we’re doing what we’re doing.
When you get past that though math get pretty fun lol
I hated this for over 20 years. Explained in 8 minutes. Thank you!
Thank you very much for this Video 🙏🏼
This was a great explanation!
Needed this 15 years ago. Thank you
you saved me. Thank you so much for this tutorial
You explain very clear, thxs
This is absolutely incredible.
wow interesting and an incredible way of teaching, i like it
Thank you so much. That was really useful
Thank you professor Dave!
You are perfect
Amazingggggggggggggggggggg. more people should watch your channel
Amazing explanation by Dave I am a math tutor... this video is perfect
i love you, dave.
Great explanations
Thank you so much!
Thank you Prof
Hello...Do we need to manually calculate the areas of all kinda rectangles and find out what value they approach? I mean, isn't there any formula..
keep watching through the series and find out!
its really helpfull
sir .thank you
Thank you so much sir
Very nice! I like it!
This is just amazing..!
thanks for this explication .
Thank you professor
I in the 5th grade and you help me understand so well 😊 thank you
We love you professor Dave
Wow that's great, thank you.
thx a lot prof. your awesome
Sir i have problem to prove a function onto and one one plz tell me something for which i can do best!!!
Thanks great lecture
Nice explanation
Thanks this is so easy
Thank you so much 🙏❤️💯💯
Nice understanding
Does a horizontal asymtote between the curve and the x-axis require any alteration to the process? Thanks
Omg. Thank you. Purely
Thanks!
I'd wait a week for the next video.
thank goodness! someone finally makes sense lol
Gr8 video professor, thanx
What the best books to learn Mathematics?
Hi Mr.Dave , pls reply for my doubt.
For circle , parabola, sphere's we have general equation.
Why polygons doesn't have any equation?
Polygons are not infinitely differentiable like circles, parabolas, and spheres. You need a piecewise function to define a polygon, because you have jump discontinuities in their slopes at every corner.
@@carultch thank you so much.
Can you explain how to apply that equation pleaseee???
1:18 The class room gives you a function .how do you get the area when a function is not know as in the shape presented ?
Ofc u cant there are no dimensions given its like drawing a square and asking u for its area without giving u a side length
u must know the function
Question- why not divide it into one triangle? (3:48)
how volume of spheroid and oloyed are correlated with their volume
TENGO EXAMENAAA
Hey anyway I could pay you for tutoring on Skype or something. Thanks
thank you
This video is GOOOOOOOOOOOOOD
Damn crit1kals really branching out these days
Can’t we subtract the area of the triangles by the area of the rectangles?
Professor Dave, if you are a patreon are u able to schedule one on one coaching for a set period of time? It would be dank if Patreons got one on one Skype time for a certain amount of time that is paid of course.
Well I do have an option as one of the tiers on Patreon where you get an hour of Skype tutoring per month! However, it is my highest tier. But it's there for you!
Proffessor Dave you game an epiphany at 3:33
Please .. tell us how to get the intergration rules like :
Intergration of x^2 is x^3/3 + C
Why is that how they get it for the first time ???
What if I see a graph but I can't discover a function out of it to integrate? I have a graph from solar power generation in a day but can't find its function. Each points give a different y(Except vertex).
Thanks
Wht about connection between differentiation and integration
mountain has a curve shape then how we split a mountain in to a bunch of rectangles, please reply if some one has the answer
split it into an infinite amount of rectangles
how you splits mountain
You don't split a mountain, it's purely hypothetical. It's an example of approximating the area.
It's amazing that Archimedes was using inscribed polygons to approximate areas of curved surfaces. If he would have taken the number of inscriptions to infinity, he might have invented calculus a couple thousand years before Newton.
Archimedes is a fake character who never existed
Ubaid Shah ..... F off idiot. F**ing clueless moron.
Robert Zanatta .. I agree.
@Leonhard Euler what does religion have to do with this?
You explained better in the first 5 minutes than my professor did in 30
Thanks =)
For better understanding give us an exemple wich has a concret ancer in m^2
Ok: a slab of concrete starts at the origin, and is 10 meters wide along the x-axis. The remaining perimeter to this width, is defined by the function y=-x*(x-10)/5, where x and y have units of meters. Calculate the area covered by this slab of concrete.
Very nyc video🙇♂️🙇♂️
thank you🥲
How to calculate incremental area under curve
Subscribed
Always make conceptualize more
OHHHHHHHH I ALWAYS WONDERED WHY INTEGRATION IS USED OR WHY IS IT SO HYPED
SO THE MAIN USE FOR INTEGRATION IS FINDING AN AREA UNDER CURVE
THANK YOU SOOO MUCH
I DONT REALLY PAY ATTENTION IN CLASS SINCE I ALWAYS DAY DREAM
relationship between function and its derivative and it's integral are how correlated with each other so we know that how much percentage are more or less they are, correlation coefficient and percentage related with real function
like volume of the spherical shape and it's surface area are derivation for round circle and sphere
now we want to know about cubic or cuboid systems that how their volume and surface area are correlated
go through my calculus playlist, it will help!
The intro was also good😂
I love you dave
You save my life
Is there anyway to find area under curve without using approximation sir.....
check out the very next tutorial on the fundamental theorem of calculus and you'll see!
I have 2 Calculus professor. One is getting paid with my tuition, the other received zero cent from me for quality lecture videos. Yet, the one getting unpaid clearly can teach WAY BETTER than the paid one. My money is clearly getting wasted!!!!
when there will be thousand of small rectangles how we well add them all? i have watch hundered of videos of you tube but no teacher can give the answer of this question
We will suppose to all like n.
Professor Dave rocks and rolls; although he looks like a rock star, he is not a rock star but a cool math teacher. 😂 💕 ☮ 🌎 🌌
Thanks Prof Jesus.
but how is it possible to find the areas of infinte rectangles and add those up
Maybe start at the beginning of the calculus series with the introduction, it explains precisely how you can do something infinite times and get a finite answer, which is what calculus is all about!
How performing integration adds area of those tiny rectangles means integration just change slope into function
whos here just to see the intro
Thank you. Professor Jesus
lmao
Just wow...
Done.