❖ Calculating a Definite Integral Using Riemann Sums - Part 1 ❖
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- Опубліковано 28 вер 2024
- 📚 Setting Up Definite Integrals with Riemann Sums: Step-by-Step Guide (Part 1) 🧮
In this video, I show you how to set up a definite integral using the method of Riemann sums. This is the foundational technique for finding areas beneath curves, and though it can be a bit tedious, it’s essential for understanding the concept behind integration.
🚀 What you’ll learn:
How to set up a definite integral using the Riemann Sum definition.
Detailed explanations of each step involved in creating the sum.
A historical perspective on why this method is fundamental to calculus.
In Part 2, I’ll actually compute the Riemann Sum to find the solution. While you may already know the faster, modern method to evaluate this integral, this tutorial focuses on the core concept and gives you a deep understanding of how integration was originally approached.
This video is perfect for anyone learning calculus, preparing for exams, or those interested in understanding the deeper fundamentals of integration. Don’t worry, I’ll also show you the quicker way to do this in future videos!
👍 Don’t forget to like, subscribe, and hit the notification bell for more math tutorials! 🔔✨
Watch now to master setting up definite integrals using Riemann sums and grasp the basics of integration!
#RiemannSums #DefiniteIntegral #Calculus #MathTutorial #LearningMath #Mathematics #IntegralSetup #STEM #MathHelp #IntegrationFundamentals #APCalculus #EducationalContent #AreasUnderCurves #IntegrationConcepts #ReimannSum
Hi all! Please post comments, questions and anything else on your mind in the comment section! While I try to answer as many questions as I can, there are more questions than I can answer by myself so if you are someone who might be able to help, please do so! The community is so much better when everyone is involved and helping each other out. Our strength is our willingness to help each other!
Also please feel free to like or dislike the video. Your feedback is always appreciated so that hopefully I can make my future videos the best possible! Thanks and happy studies!
with this video i finally understand this stuff thank you so much
This man posted this video in 2009 and still willing to help out and answer comments a decade later. The 🐐
Ad -"are you really trying to learn math from videos published in 2006"
Math doesn't change every year bro
Brady Ho No, I am trying to learn math from textbooks published in ancient greece
@@benzhang9186 my school doesnt bother to update their books so these videos make sense
Cuz these are fundamentals! If they somehow changed, the entire mathematical world would be in chaos for better or worse. Math does change every year, but only the very advanced stuff that goes way over my head personally.
new pre-school math: "Am I a joke to you"
It is always very interesting to see people on UA-cam who are a lot better than professors at universities, such as Patrick.
+Kingmodder well, I used to teach at university
Haha, yes, and probably most of your subscribers would wish that you were the one to teach them (for instance me) ;).
i do this in high school :(
Some people who good at something not necessarily good at teaching
Kingmodder exactly..
you're my favorite math tutor on youtube, thank you thank you! Always very clear and helpful with your examples. YOU ROCK!
the point can come from anywhere inside of the interval. the point is, as n goes to infinity, the intervals become so small, it is basically the same y value no matter where you pick the point to be.
SUBSCRIBED!
I swear, I LOVE EVERYTHING about MATH EXCEPT FOR RIEMANN SUMS. Butttttt, Thank you for explaining gazillion times better than my instructor! I have a test next week and this is like the only lesson i am not getting until i saw your vids.
Conceptual understanding of the basis of integration is one thing, but why would ANYONE do this voluntarily? CHRIST! I have to teach this soon so this video was a great help. Question though - can you use the almost formulaic approach you used here with those summation results and the riemann sum limit definition? That would be much easier to teach than going into all the BS I've seen in other riemann sum videos. Thanks for all your great work and please keep it up :)
"Don't talk to me or my sums ever again" - Riemann (1865)
TEAM LAST MINUTE💀🤡
Watching this in line for my exam
Thank you for the video sir. You managed to teach me more in these 6 minutes than my professor did in an hour.
Thank you so so much! I cannt explain how grateful I am that you take the time to make these videos, and that they are free too! Nevermind the expensive online tutors or khan academy, who's videos are half an hour for one sub-subject. I've been watching your videos since I was a sophmore in calc 1, and a clueless one at that! No matter how many times I've been in for help from my teachers, none of them could explain these concepts as well as you have! You're a remarkable teacher, Thank you :)
Taking the Ap Calc AB exam tomorrow, this video is a great refresher, now I have nothing to worry about! Thanks for sharing your awesome teaching abilities one the internet!
I took a weekend to learn this , but then i forgot it again. After seeing this video , i now know it again. Thanks !
patrickJMT is my best friend, always helpful and never leaves me hanging
you made learning 6 chapters of integration in one night possible! You are my hero!
This was so so helpful, I had tried to understand sigma notation for riemann sums for so long and this is the only thing that helped. The best!
@patrickJMT
yeah. you should get an award or something too!!!!!
I'm totally nominating you for teacher of the year!
@shahzun haahh shirts for everyone!
plus, if we do bad on the exam, that just means we'll be better prepared for calculus classes in college! the important thing is we try.
thanks for the help patrick
to calculate Xi, u used a+∆x, and that is for the left endpoint, but what about the right endpoint or the middle one? what is the formula?
if u could answer me this question it would be greatly appreciated :)
thx in advance
You got me through my first University unit, thanks heaps!
I dont understand too much enghlish but you are so good teacher that i dont even need enghlish language!!. thank you now am lill bit smarter :D
What exactly does "x of i star" in this video represent? The way it's calculated is giving me the right interval point of the rectangle.
@Eneas724 lol, thanks.
patrickJMT, thank you soooooo much (really it would be infinity long tons!!!)
You are the finest, greatest, top, foremost, leading, preeminent, premier, prime, first, principal, supreme, of the highest quality, superlative, par excellence, unrivaled, without equal, unsurpassed, peerless, matchless, unparalleled, unbeaten, unbeatable, ultimate, incomparable, and perfect in my math life 8D
Excellent video. I'm going to recommend my physics students to see it. Hi physics students! Also the sum formulas are easy to find elsewhere on the internet and are easily proved by induction. To come up with the original formulas you can use the k^3 - ((k-1)^3 trick found in Spivak.
Thanks so much! My teacher skimmed over this and this helped me a lot.
Can reimann sums be used without a function, just points on a graph? Let's say I have 30 points on a graph, to calculate the area, will I have to do middle,right, and left endpoints to get it? Or can I use reimann sums?
@MonaRocks09 hey mona, some people just are pissy people and like to argue and criticize others. do not let some d-bag on the internets piss you off ; ) some just having nothing better to do in life than to try and feel important and pass their misery on to others.
yes, this stuff is a bit tricky the first few times around
exactly what i am looking for, thanks man
this is awesome!!thanks for posting... Do you by any chance have a video with an example where the function goes below the x axis???
Patrick it is nice to see you are left handed, just as I am
I missed one class and so I ended up here lol this saved me 😁
This is really helpful! Especially the equation part. Thanks
I have a test on this today. Thanks for this great review!
Patrickjmt, your the best at explaining math thank you very much.
Zeno1999 a hero is respective to personal opinion so I don't see why your trying to be so technical about someones comment. He is praising the man so just let it be.
is this right hand or left hand or mid sums? and do the Rieman formulas differ for these 3?
thank you patrick you are such a nice person
your videos are very helpful. thanks.
I know I already asked you, but how do you get n(n+1)/2 from the sigma notation?
Why do we use the formula a + (delta x)i to calculate xi*?
For those who don't realize how in depth and complicated this subject is go from 0:11 to 1:10.
Rusty Shackelford its not that hard of an idea
YES!! this is exactly what I needed!
it's in english but i understand, nice, thx
Deadweight of society
man , i got this by just watching your video, and i couldn't get all that with one and a half hours of class , and my native language is spanish.. so you get the idea how crappy my teacher is :(
Thanks man, God bless you. You should write a book!
Thank you Patrick, very much
so well explanation, thanks
+patrickJMT, I have a question that says find the riemann sum of f(x) with an inifinite number of intervals. Do I calculate it using this way?
My calculus teacher says he's your good friend
@fremsley001 I just randomly busted out laughing in the middle of the library. Thanks :)
I have a question I got in my class- e^(2-3x). And I had to integrate it using this system. Still can't do it. Help?
thanks brotha! Great job on the vid.
wait a minute... Don't you factor out the (1×2i/n)^2 through the FOIL method
Great stuff, keep it up !
So that's what JMT stands for!
My very quotable teacher in Fourier analysis said that it's a disgrace to associate a big mathematician like Riemann with the depraved definition of integration that is the Riemann integral.
Why does the sum of i from 1 to n = 1/2 n(n+1)
Thanks this really helped
would be nice to see one using the left hand side...because its i-1 ....
Thanks Patrick, you rock
This guy is the goat..
Nope, right, left and mid sums are all completely different. Those are estimation methods where you divide it into rectangles and add it up. Well, this is also rectangles I guess, but delta x is so small that it's not a number.
very nice explication
We never learned these in calculus 1. I’m in calculus 3 now
this is awesome, patrickJMT...please have my babby...as soon as i find out how babby is formed :(
thank you for not stuttering every 3 seconds like Khan Academy
and repeating yourself every other 6 seconds
happy i could help :)
also, when programming, a program must calculate an integral using this method, so it must be programmed in this way.
This was an amazing tutorial I was really pondering about this, but the way you write the sigma is so weird.
OMG THANK YOU SOOOO MUCH!!!!! it legit saved my life :)
what's the difference between definite and indefinite integrals??
indefinite intergrals have no upper and lower limits of intergration
i.e, its not intergral from a to b, its just intergral
k
Akali Or just finding the antiderivative to put it another way.
To add to what @vereand said, definite integrals are actual values, while indefinite integrals are functions.
Every video I watch there comes a point where I hear the phrase, "I'm not going to explain this, it's not my intention." Well wtf.
thanks a million
@Flaminheartx3 DON WORRY! you could do it. i never read HS calc books, just watched these vids an hour b4 the test and aced it. ^^
Thank you man!
No problem!
I hated these problems in high school and I still hate them in college.
You must NEVER take down the website, or stop making videos. You almost single handedly taught me College Algebra due to the feebleness of my prof., and now I still use your videos to study in Calculus. You're like Jesus with a whiteboard.
Reimann sums could not possibly be more useless. The exist solely to be translated into (the vastly superior) Sigma notation.
im thinking of doing maths at uni, does anyone know any jobs you can gt with maths
u just forced me to subscribe to you !!
FYI: i usually do not subscribe to anyone
Once you go pat, you don't go back
Shoutout to anyone else here for final review.
Why do we have to learn this if we can just take antiderivative
is he a computer scientist? whats with ending stuff with semi colons.
24 people must of been in a bad mood to dislike this video...
I'll Riemann your sums.
wish u could take my quiz for me man. lol
AP Calc today!!
you > khanacademy tho.
fr nigga
Mad W
They're both good... they can coexist...
why u trynna start some fake beef?
Both of them are great, and they have their differences. I like Pat because he jumps straight into the problems, whereas Sal takes his time and explains the problem in detail and how that problem originated (which isn't a bad thing, but most of the time I prefer to just see how it's solved if I already understand why it's important). If I'm really struggling with a concept, then I go to Sal.
if you want to see where the formulas come from watch the video about 'the definite integral - understanding the definition ' that is listed on the right.
where r those videos
Dem video r n deez channel.
ha! - one of the best comments ever : )
I've literally spent the past 6 hours going through sources trying to understand the Riemann sum for my year 12 Maths assignment, calling up friends in uni and going through their text books, and this one simple video explained what I couldn't understand for 6 hours in 6 minutes. You, kind sir, are a life saver. Thank-you so much!!!
I remember watching this back in 09 when I was in school.
So glad this guy blew up.
Thanks God to let me find this channel.
Peace upon you
I'm taking calc 1 and Patrick's videos are extremely helpful. so I definitely agree with you.
AP Calculus test on Tuesday anyone?
Anthony Pipkin yeppp ab
Monday
You have been the biggest help in all my college math courses :)
Hi all! Wanna help a UA-cam education OG? Please post comments, questions and anything else on your mind in the comment section! so, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly as it helps me :)
@halospartan5 women dig guys that can do math
thanks a bunch ben. i keep making these videos cause of comments like this :)