❖ Calculating a Definite Integral Using Riemann Sums - Part 2 ❖
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- Опубліковано 28 вер 2024
- 📚 Setting Up Definite Integrals with Riemann Sums: Step-by-Step Guide (Part 2) 🧮
In this video, I show you how to evaluate the limit form of the definite integral for this example.
🚀 What you’ll learn:
How to set up a evaluate a definite integral using the Riemann Sum definition.
In this part, I 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!
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Congratulations, you may be the first and only lefty to do an entire problem on white board without smearing any of it. From one lefty to another, props.
I always have to write awkwardly when i get to the middle of the white board to prevent smearing.
Then learn to write correctly... To write right, if you will.
Uncomfortable Truth i don’t know the left just feels better and more justified to me
it is hard for everyone, myself included.
you all only see the end result after thousands of hours of study on my part... and not all the frustrating moments getting to where i am now
I needed to hear that, thank you.
How many hours do you work? Do you ever sleep?
Not for me
You've become a integral part of my math experience.
"WELL NOT NOT LAZY!, JUST CLEVER!!!" lol...very true
best explanation for Riemann sums~!!! was stuck all day yesterday until i came across your videos and clarified everything in seconds...thank you
I feel like i've wasted so much time trying to understand these problems... seriously, just watching 15 minutes of video and it makes crystal clear sense... simply amazing.
I have to say, I have been watching your videos since I am prepping for my college final in calc and you've helped a lot, especially with this integral stuff.lol thank you
Did this in my calc class...the prof messes up every time has to be corrected by students. Was beyond confused but makes sense now. You're amazing.
Cool, calm and clear. Why can't lecturers see this? :) Thanks for this. I missed the first three days of my lectures for calculus, flu does not play nice, but thankfully clued up now.
Great teacher !!! preparing for my final exam in less than 7 hours hahaha
Late response, but did you do well on the exam ?
yea i did okay !
nice
More like 30 mins before the test 😅
hahaha mines more than 3 weeks away :/
Oh my god, you are one of the only people I could find who actually demonstrates this in a way I understand. You have my gratitude.
Thank you very much for the help. My high school Calculus teacher doesn't really teach how to do a problem, he just does it on the board and then gives us homework. I've tried reading the book too and I can't seem to make sense of it but you finally actually TAUGHT me how to do it. So I say again: thank you so much. :)
Thank you for taking time to broke down the equation step-by-step. It was long and confused process, but you made it simple and understandable. Thumbs up!
Our class wasn't taught Riemann Sums in class to the point where we were comfortable, and I have a test this morning where one of these calculations is present. I now understand them thoroughly enough to navigate through a Riemann problem, and I appreciate your help in doing so. Thankfully I found the video just before the test this morning, we'll see how it goes!
Best regards,
B
Amazing, worked for hours and never came to understand this at all, now after watching the video I think I've got it, Thanks!
Not going to lie, I love watching your videos. You don't go too fast, but you also don't go too slow either. Perfect combination, I have a good calc teacher actually, but my class is so distracting we can't get anything done, glad to have you as back up. YOU and Khan of course.
Wow!! woke up at 2 am to watch this and it paid off, Thank You Patrick you just make Math easier :)
Thank you so much for creating this video. Self-learner here so I do not have a professor I can go ask. These two videos clarified a lot of things that I just was not getting from reading Stewart over and over.
Your explanations are vivid and clear as crystal
Thank you for explaining this. My professor was kinda vague when she taught us this. I couldn't understand how everything plugged in and worked together, but now I do. This video helped me out a lot!
You just made my day. You explained this very clearly and explained how you did certain parts.
Wish you were my instructor
i have learnt so much from you in these 2 vids than i have in my lectures.. thanks
thank you so much sir...i'm in college now and the professor is so fast, but i understand you perfectly. this was very very helpful! (now i can breathe)...God bless!
thanks for this video. the concept really clicked after watching it. your explanation is very thorough and clear.
dude, thanks a lot. I have an exam 4 hours later and you make me understand this in 10 minutes
Good Job Patrick.
After 7 years Your instructions are still helpful.
Absolutely perfect man. I have a calculus final coming up, and riemann sums were something we did at the beginning of the year, and my instructor spent about 2 class sessions on it, so needless to say, I had no idea what I was doing. Your video did a great job to explain just what I needed to know so, thank you!
TheYourfaceable lol my professor spent 30 minutes on Riemann sums.
a whole week in class and couldnt understand this rule , yet i understood here ... thank you so much :)
So, I feel a little dim-witted asking this, but, the formulas you get for the summations of i and i^2, those are derived by taylor/maclaurin series right? Excellent work by the way. I've had two semesters of calc already, but they were taught by a truly rigorous professor who, although displaying a thorough knowledge of his field, I think expected to much out of his students. You do an excellent job of bringing all of this down to an earthly level.
@naytus thank ya
wow thanks pat, my instructor did a terrible job explaining how the lower powers within the numerators cancel out, awesome !
@Nedorostok glad i could help you : ) come back any time
1:46 *I move away from mic to cough*
colangelog09 chocolate rain!
@@zain4019 I hope you failed your calculus
I spent so much time going through this dumb concept in my book and I was so confused! but you cleared it up and helped me solve my problem, thanks!
you are wonderful! I just have one question. I am just learning integrals and I just want to know why we have [(n)(n+1)(2n+1)]/6. Is there a rule that I have to follow for that?
C.E.B. C. That is simply the equivalent of Riemann's sum of i^2 . Same with i^1 = [(n)(n+1)/2]
Thank-you This made so much more sense than when my math professor was teaching it.
This shit is so hard for a slow brained turd like myself
Finals week, lovin' it. Thanks Pat.
Thank you so much!! Your videos are truly helping me pass rather than fail my finals! O_o
Dude, you freak'n rock! Love your tutorials. They're so clear and simple. I wish you were my Calc 2 professor!
Those are some quite neat summation notations!
I LOVE the way you teach! it's super clear and I understand everything!
THANK YOU FOR ALL OF YOUR VIDEOS AND YOUR TIME!
now what are you studying
Patrick, first I want to say you do a superb job with your videos. Your final comment that some how by doing a page of Riemann sum formula manipulations will give the student a better understanding of the Integral is an alt fact that math professors have been using for decades to justify abusing the student with the Riemann Sum definition. First you have the x-sub i * formulas that just come out of nowhere. Then there is no referral back to the Integral method showing why the two are relative. Lastly this is why Leibnitz and Newton invented the calculus Integral because they saw the relationship and saw that by integrating each term, they did in fact get the same result. They devised the rules of integration to accomplish quickly and efficiently the Summation value. Of course the Professor's fall back is that there are functions that you cannot integrate, but what I discovered is that Riemann can't do those either.. But I appreciate your trying to make the student feel a little better about having to do Riemann Sum. Keep up the good work.
wow amazing u make understanding riemann sum alot easier than the txt book does
hi patrick, i have a question. it is (a+ delta x i) if it is right hand point. it is (a+ delta x (i-1)) if it is left hand point. what is it for mid point? thanks
Thank you so much, I missed a couple days of AP Calc. and couldn't figure out how they were doing theses based on my friend's notes, but you made it really easy to understand.
Also,do you have a video on how to do this with the "short cut" using anti-derivatives?
You are a legend. Super helpful for my exam in 3 hours!
Wow I thought this was so hard, it's not even that bad...thanks a lot!
unfortunately my teacher is HORRIBLE at explaining things in calculus. thank you so much for posting your videos...without them i would be beyond lost. :D
Hi there. Your video greatly helped me. I have just one question. On my homework, I was asked to find the integral using Reimann's sums and with right endpoints where n=8. how would I go about doing this?
Just wanted to check, at 7:25 I think you meant to say you are adding those first 2 terms right?
Any more vids with examples of how to solve definite integrals using the limit of Riemann sums?
Wow, thank you so much for taking the time to explain this very thoroughly concisely! I was having such a hard time with this!!
thanx for the vid...it'll help me alot to pass my exams tommorrow
in 4:50, by applying lim tends to infinity, you can turn all the terms with n in the denominator to 0, leaving you with a solution of two. i dont understand why you carried on onto the next step.
The final answer isn't 2, it's 20/3.
All the terms which had n in the denominator at 4:50 were being multiplied by terms which also had n in the numerator; if you'd turned all the terms with n in the denominator to 0, you'd be multiplying them by terms going to infinity which is indeterminate.
This got me through a brutal question on my Calculus final! THANK YOU!
nope. i have taught a top a 20 university for a few years, a community college for a few years, and two places in-between.
i have no desire to go back into a classroom any time soon.
Thank You very much i was struggling not knowing what to do..... may the Lord richly bless You....
Hey, thanks a lot for the video. I only have one doubt, do you have some theory videos? like, where do you get the equivalence of i ? (i haven't checked the rest of your videos, so excuse me if the theoretical explanations are there)
he solved better than my teacher ,I'm gratefull.
@patrickJMT can you show an example where the exponent is not alike?
@7:12 can you tell me why exactly you separated the coefficient 2 from the limit of (2n³ + 3n² + n)/n³ ? Is there a specific rule that explains how it works? Could it be that we only the limit of the highest powers ?
@Zyntle ya i know what u mean, its waaaaay simpler than when lecturers say it
Thank you, this just helped me with my homework and my quiz due tomorrow. =)
if f is continuous on [a, b], or if f has only a finite number of jump discontinuities, then f is integrable on [a, b]; that is, the definite integral fxdx exists.
Can anyone tell me in simpler terms what this theorem means? Thanks!
Perhaps you could break it into i and i^2 then put the two formulas into series? Just a guess though.
You're a lifesaver. Thank you!
if i get an i^3 and I know that the summation equivalent is [n(n+1) all over 2] squared what is the process of factoring that out?
Do u have a video of going from summation to integration?
Thank you for posting this, you're a life saver dudeman!
The only difference is you make the summation start at i=0 instead of i=1 and end it at n-1 instead of n.
So the formula's will change a bit. Just make sure you minus 1 from every n!
Example:
Summation of i becomes (n-1)(n)/2 instead of (n)(n+1)/2
Extremely helpful. Thank you very much.
@jessiesun1142 ha! tell him / her that i said thanks for using my stuff!
Thx!!!!!!!!!!!! IT REALLY HELPS ME A LOT, VERY CLEAR!!!
i expand where you said we should be clever and I have a 3 constant so why you have 2 for the answer?
U have open my mind. Thank you very much ❤❤
Thanks a lot Pat. You are amazing.
I just want to know what is the point of this if we already have integrals
whoa... this is mad helpful... thank you
Sir.. May i know.. Is it i squared = n(n+1)(2n+1)/6 or n(n+1)(n+2)/6? Which is true?
On the second step, why skip to solve that last piece of the second step?
This was so helpful!!!! Thank you so much!
You are a genius. Thanks so much
Thank you so much... I almost gave up on trying to be a civil engineer
@barbaric37 come back any time! : )
I dont know what to tell but thank you so much!!
@dgizowski Thanks for comments definitely one of the best videos of Parick
I give 5 starts
Thanks for the help!
Great video! Thanks for the help!
OMG thank you! you made this super easy!
How do you find the lower estimate?
Awesome video, thanks!
Thankyou so much, you're amazing ♡ needed this for my ap m
This is lovely. Thanks a lots !
This is reall helpful. Thank You :)
how do you find the formula at 3:37 ?
I don't get that part
how did u get the (n)(n+1) and (n)(n+1)(2n+1)
Thank you!
Thank you
thank you so much!