Riemann Sums - Left Endpoints and Right Endpoints
ฝัง
- เผยแพร่เมื่อ 13 ต.ค. 2024
- This calculus video tutorial provides a basic introduction into riemann sums. It explains how to approximate the area under the curve using rectangles over a closed interval. It explains how to determine the area of the region using left endpoints and right endpoints. The area under the curve is also equal to the definite integral of the function over the closed interval. The area can be approximated by taking the sum of the area of each rectangle. You can express this using sigma notation and calculate the sum using the appropriate summation formulas. The area of each rectangle is simply the product of the width and the height. The width is delta x and it represents the length of each subinterval. The height of the rectangle is represented by y which is a function of x or simply f(x). The average of the areas using the left and right endpoints is very close to the actual area under the curve. This tutorial contains a few examples and practice problems. The area using left endpoints is an under approximation or lower sum and the area using right endpoints is an over approximation or upper sum when the function is increasing. The upper sum is the higher of the two values and the lower sum is the lower of the two values.
Antiderivatives:
• Antiderivatives
Basic Integration Problems:
• Basic Integration Prob...
Indefinite Integral:
• Indefinite Integral
Definite Integral:
• Definite Integral
Differential Equations:
• Finding Particular Sol...
_______________________________
Properties of Definite Integrals:
• Properties of Definite...
Rectilinear Motion Problems:
• Rectilinear Motion Pro...
Sigma Notation - Calculus:
• Summation Formulas and...
Riemann Sums - Area:
• Riemann Sums - Left En...
The Midpoint Rule:
• Midpoint Rule & Rieman...
________________________________
Finding Area - Limit Definition:
• Finding The Area Using...
Definite Integrals - Geometry:
• Evaluating Definite In...
Fundamental Theorem - Part 1:
• Fundamental Theorem of...
Fundamental Theorem - Part 2:
• Fundamental Theorem of...
Net Change Theorem:
• Net Change Theorem - C...
__________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections
Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
Next Video: th-cam.com/video/5XreKMJDJsg/w-d-xo.html
442342uu343434324342351
Thanks dude
in conclusion, organ chem tutor and khan academy are getting me through university
Honestly
same lmao
@@ericcartman1168 We all know how it goes, everyone's capable of mastering anything on their own but if you want the job you gotta have the Golden paper that proves you're a bit less stupid then when you were born ahahah Not hating the system tho, there's a lot of good teachers out there I personally I can't complain much
@@ericcartman1168 the teacher is just motivation to learn
In conclusion, you're cute.
After a whole day of not understanding this concept by my Math professor's slides (at University even), this explanation explained everything in a few minutes. It is truly the epitome of studying smart.
I completely agree, I have a pretty good professor all things considered. But I need glasses and haven’t gotten some yet. Not being able to see the board makes it nearly impossible to fully grasp.
@@mocapcow2933 try seating upfront tho?
@@railx2005 you will not control me!
I'm from Germany and my German video essays always confused me, completely talked past the subject and also missed the point. I was treated like an idiot. I decided to give an English video a shot and I was very pleasantly surprised. Nearly every question I've had has been answered. This channel might be my turning point in terms of understanding math in school. Thank you!
This man just summed up (pun intended) two 50 minute lectures in 20 minutes. :) Why do we even pay tuition?
PaulyM856 HAHA I AGREE
bc college is a freaking business and wants to milk money from people bc they knew they can :\
Would you learn this without going to college? I agree some teachers are absolutely useless teachers but if it weren’t for school, I wouldn’t even look up this video and try to learn about it.
@@mordecai8707 More valid and real-life scenaro is you cant say I am good at (insert job) cuz I learnt from organic tutor or blah blah they need a frickinn valid degree..(i dont like this system but thats how it plays out in real-life for atleast majority of the jobs and def the one with degree is preffered always..I see it in my experience)----Plus if ur wondering a great company like google def said it doesnt care for a degree right? Wrong i know ppl on the inside who do have a tending bias towards one with degrees cuz apparently it means a person is 'serious' about their job and went to uni and paid hundreds of thousands of tut fee towards rather than a 'lazy' person who didnt go(even tho he might be better in skillset sometimes)
Higher ed is a scam
I go to UofT and I must say you are a much better teacher than the profs here who are earning 6 figures.
Bro I go as well and have to literally rely on his videos. (Exam is tomorrow lol)
@@imtherealgandalf3490 good luck im taking mat133 wbu
@@aditsud5354 hope he replies soon...the legend27
I'm in 136 rn, and I have NO IDEA what's going on cuz this stuff isnt even in the textbook
I'm from UBC, same here lol
You are so good at explaining.. I’ve learned more from this channel than from my professor. Thank you so much
There are not enough words or time in the world to represent the amount of appreciation I have for you and the content you create. Thank you
in class, i can clearly see how my teacher demonstrates this lesson on the board but i'm still having a hard time understanding the topic. but you, on the other hand, i cant see you, you are on the other side of the screen doing this, yet in just a span of 7 minutes, i now freaking understood the whole freaking thing! gosh you saved my life!
I finsinished spring semester about 3 weeks ago and got an A in calculus 1. Now i'm in summer semester doing calculus 2 and you are still carrying me through, thank you so much organic chemistry tutor. I've never been so confident about math
Every time I hear your voice, I know I'm gonna be okay. Can't thank you enough.
Hi Organic, I'm having a hard time in Calculus 1 and this video helped me understand a little more. Thanks!
Why can’t our teachers just be like him?
@@JH-ux1re Yeah, it's time for us to be like him ;)
I wanna say the freakiest things to this man my professor has made calc 2 seem like rocket science but your 20 minute videos are more useful than two hour lectures
Do you have a patreon or something? Because I would gladly donate, etc. you are awesome
I do. here it is:
www.patreon.com/MathScienceTutor
Hell yeahh!
Yeah, why not?
There is no level of describing how amazing your videos are. I first watch your videos before reading the textbook. Really no words^2.
Learning from your channel is so much better as i actually understand the concept in such easy way you explain it all. I've learned more from you than school. Thank you
Thank you so much, this made it crystal clear for me. I am in Calculus 1 and geometry and graphs are not my favorites so when teacher started making random rectangles under graph and tried to finish unit as soon as possible I was a lost cause. This however makes it so much easier and basic concepts looks so challenging at first in calculus because of new signs we use to express the functions and other expressions...
One day I will get a job & donate to this channel.
Have you donated yet? :)
@@EmpyreanLightASMR still unemployed 🙂
@@mehedihm Oh man, that's awful, i'm sorry to hear that. I hope everything works out for you soon!
@@EmpyreanLightASMR Thanks man. Actually I was in my first year of engineering when I watched this video and wrote the comment. At that time these tutorials were very helpful for me. Now I am on the final year.
donated yet😉
No joke I had massive homework and projects in my Accounting / INFS courses and completely ignored and fell behind Calc these past two weeks. Test tomorrow and this tutorial helped a big amount on my study guide. Thanks!
You’re a literal life saver for me when I have a math exam. Thank you so much and may God bless you.
To be honest, you explain math better than all professors around the world do. really you are amazing thank you so much
You're the only reason why I am getting through my university. Thank you for explaining everything so well
Organic Chemistry turned out to be one of my best and most successful pursuits, class-wise. Partly the way my brain operates, but also partly due to an awesome female professor who had a way of explaining everything. Between organic chemistry and logic, i was good to go! lol. Couldn't believe that such a class turned out to be a strong suit for me as someone earning a degree in English Literature. Thank you University of Delaware for providing a professor who helped students easily love organic chemistry. I can't tell you what it meant to me, seeing the more superior not do as well as they went on to become veterinarians and such....they said it was a weeding-out kind of class and of all people, little inferior me rose above all the know-it-alls!!!!!!!!!!!!!!!!!!!!!! Aaaaaaaaaaa! I kind of needed the confidence boost to be honest and couldn't be more appreciative that some mysterious force out there wanted other people to value me instead of ignore me. And, finally, this many years later (51 years old now believe it or not!) and I created a youtube channel. Quite a feat for someone with extremely low self-esteem who never spoke much and towed the line for her male counterparts, big time! YAYYYYY! Just needed to vent for a second. Thank you and I LOVE ORGANIC CHEMISTRY! 👑💗🐰
It improves the understanding of integral by meticulously comparing the left and right Riemann sums with the definite integral. Thank you for the work.
You are a blessing. I wish if there's someway I can compensate for the videos you're providing. Keep it up my man.
donate
Professor Organic Chemistry Tutor, thank you for explaining the basic Introduction to Riemann Sums in Calculus. This is a solid and old fashion way to approximate the Area under a curve using rectangles. This is an error free video/lecture on TH-cam TV with the Organic Chemistry Tutor.
This is my first time to hear about this topic and I learned it in 20 minutes from this video
You lecture me even to my dreams. What a wonderful tutor.
subscribing at your chanel was one of the best decisions i have done in my life
Out of all the resources that have helped me understand and get through calc, you are by far the best
Bro youre honstly the best, you have vids on everything under the sun and explain it so well. Helped me so many times already, really cannot help you enough
Thank you for explaining on how to draw left and right endpoint clearly.
The way u explained this concept damn it's so good 😃😃
This video helped me understand this topic sooo well! Thank you!
This man single-handedly has gotten me through calc
Really good explainer. Also explains how increased bit samples (n number) results in higher audio fidelity (as an approximation of analogue signals)
I understand this better than the way my professor teaches. Thank you!
Thank you so much for your videos. They are so helpful. I just needed some light on integrals. Please, keep doing it. I have maths exams. Engineering , part 2 and part 3.
i make sure to click on the ads on your videos cuz u deserve it!
Thank you! I was just struggling on this for like an hour lol. Im trying to pass the AP calc AB test next year in 8th grade. This definitely helped.
What a wonderful video. Thank you for your clarity and the by step approach you take to all your videos.
i made a google account to like and subscribe to this video , ur explanation off charts man keep it up
This man explains better than any teacher I've ever had
How are you this well educated on so many topics? You seem to have every single STEM major covered lol
@Abel Tatek, that is pure communication skills. many well-educated people, higher IQs having hard times trying to explain their ideas. but this dude knows how to put every topic he discusses in the simplest form.
@@pilatopolea6558 we gotta protect him at all costs
it's year 2022 and this guy's still saving lives.
Nearly 2024 now
2024 saving mine rn
I have a test tomorrow and you have just saved me, love you lots :heart:
wtf in uni for physics and realising that I didn't understand calculus at all lol. Seriously a lifesaver
Sir you are the hope of every engineering student
You teach more in 20 minutes than my maths teacher does in a week
Thanks for hard carrying me through school
Best explanation so far....
This is an underrated channel that ppl didn't know, IT HELPED ME SOO MUCH W/ PRE-CAL A&B AND CHEM!!!
it has almost 6 million subs. it is not unknown at all lol
thank you best explanation ever better than clg professor ;)
You just saved me again. Thank you for your lessons, cheers.
This explanation helped my nephew focus and understand
This your lectures are extremely great, just helped me out with this explanations
Organic Chemistry Tutor just bailed me out again 😌
As i realise maths ain't bad because of you🎉
How clearly he explained 👏
absloutly brilliant , you helped me more than doctors in my university(ain shams cairo).
10 times better than my professor. Thanks!!
how does this guy know literally everything
Excellent presentation of a topic which looked very difficult.
Very informative explanation
damn 20 mins video is wayyyy better than a few classes from my math professor, I go to UBC
Thank you sir.it was so easy to understand
Great video, thank you so much
this explained it WAY better than the professor
Love it! You're just an amazing teacher, did you know?
I always wondered what man with a sexy voice like this helping me throughout my years looked like
you are a life saver frrrr 😭
I noticed that when you double n, the percent error decreases by the square of n. So, 8n is twice as much work as 4n. However 8n's error% is 25% of 4n's error%. So, 8n is 4x as accurate for only twice the work.
Can you show an example when the number of rectangles(n) are not given? that's the types of examples i'm doing at class. I seek your enlightenment for this topic, sir organic chemist master sensei.
I know this is a year late, but if the number of subintervals isn't given, shouldn't you assume that it's infinity? If the number of intervals is infinity then the way you solve the problem becomes totally different. Either way, if the question doesn't tell you to use riemann sums then it's better both in accuracy and in convenience to just use integrals.
@@skinach Interesting, your comment is a nice find. Will try to keep this in mind if we're given similar problems (like not being told to use Riemann sums). Just in case.
love the content❤
My lecturer taught me this and confused me…. thanks very much
thank u a lot , you are really a life saver man
you, sir, are a godsend!
Thank you for this video. It helped a lot.
Excellent video. Thanks.
Thank you that helped me so much
you are amazingt thank u for existing]
Currently watching this video while my professor teaches online bc these videos are better 😂
organ chem tutor your are an angel from GOD
Greatly appreciated, keep it up!
Oh my gosh I finally get it.
Great explanation!!
You better then me back in my glory High School days
Their is a reimann sum equation in geometry book very similar to it. N(n-3)/2. It a diameter of a polygon sides n represent the number of sides in reimman sum terms n(n+1)/2. No college math prof will mention it
My guy you're literary saving me here 🖐️
Love your videos
Ur my favorite fr
Thank you so much
Very good. But why does taking Anti-dervative of function also give U the area❓It doesn't seem to be related to the method of using Rectangles.♦️
This is amazing; just started integration and this video really helps give an intuitive view.
greetings, the channel membership is way too expensive, especially for people living in third world countries (like me). if you could somehow help us out it would be really great
Thank you very much ❤
me having a mental breakdown while O Chem. tutor is trying to explain calc to me
you are a legend
thank you homie, bless up
In your first example in calculating the area, why did you use four rectangles?