Midpoint Rule & Riemann Sums

This calculus video tutorial provides a basic introduction into the midpoint rule which is used to approximate the area under the curve. This video explains how to use the midpoint rule to estimate the area of a region using rectangles and how to confirm the approximate integration by evaluating the definite integral over the closed interval. The definite integral gives you the exact answer for the area of the shaded region. This video contains plenty of examples and practice problems on the midpoint rule and riemann sums.
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-tutor.net/
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Next Video: kzbin.info/www/bejne/maWooX6Qrt2kfLc Final Exams and Video Playlists: www.video-tutor.net/

[@danielukpe4851]

My Guy you literally saving my degree here

[@kashleyvlogs8345]

same lol

[@mrjustin2607]

same here

[@godlytechreviews4]

@Kashton Alexander lol

[@godlytechreviews4]

@Carlos Wilson I will try it

[@etiennekruger]

Not me paying my lecturer so that this guy can teach me 👀👀

[@xiongchristy]

Thank you so much. I’ve been struggling with calculus, and it has really made me questioned if I should keep going. After watching your videos, I felt a lot more confident and comfortable with calculus. I really appreciate your time in making these videos! ❤️❤️❤️

[@rubenrenteria8542]

Your the reason I'm gonna pass calc, I hope you understand that your doing what some teachers cant

[@jacobb6973]

yo'rue*

[@RizStar-yn4yf]

@@jacobb6973 you’re* 💀

[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for another exceptional video/lecture on the Midpoint Rule and Riemann Sums in Calculus One. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

[@nicholasmaloof8378]

How could you dislike his videos :(

[@cassied9327]

I always just imagine them hitting the dislike button in some sort of freak accident. 😂🤷🏻‍♀️

[@danivinu8701]

Some men just want to watch the world burn

[@euclid9492]

You, Patrickjmt and BlackPenRedPen are the best Calculus youtube channels! I am going to college online and having these videos really helps! I don`t like it when people talk down about their professors to lift up youtube teachers, but I think that these videos are key to feeling comfortable with these techniques in practice, as most professors only have time to really go into the concepts and lightly touch on techniques. Thank you for offering your help!

[@chikanmao8326]

Yes and also maths for thought

[@bs7363]

Don’t forget Brian McLogan either, he’s a real G

[@chriswilliams5291]

I have been watching your calc videos to prepare for calculus one that I will be taking over the summer. I really appreciate how you're so good at explaining difficult concepts. Not only is finding the definite integral faster, but it is also the actual answer. It makes it harder to learn the longer methods such as the midpoint rule knowing that the answer is less accurate and takes longer, but I guess if we have to know this for calculus it's worth putting in the extra effort.

[@anicredible2765]

I have to worship you every single day. I just got my math result. I got GPA 4 for calculus I and II. Glad that u exist.

[@_blueshift_3976]

Im very appreciative of your videos man, keep up with the great work...

[@jillchan167]

You are totally awesome. How I wished all instructors teach as you do. Thank you, your tutorials really are such a big help. Hoping you could make some videos regarding abstract algebra. 😊

[@johnettipio]

Another thorough and understandable explanation, your videos have been very helpful. Merry Christmas!

[@LudwigSpiegel]

Beautifully explained!

[@architect8675]

Holy shit, thank you so much bro, I have been navigating the whole internet searching formal numerical menthods for improper integrals and you have gave me the last pice of information I needed to understand the segmented quad rule for infinite integrals.

[@mishaldurrani125]

Thank you! I love your videos

[@achingaster1199]

Thank you. I missed class today, and I was going to cry over homework I couldn’t begin to understand. You made it better.

[@arwinsepahram9181]

One of the best people to ever walk this Earth. We love you.

[@davidkwon1872]

Jeez, your so good at explaining

[@jeremyhopkins4622]

You are better than khanacademy Im so glad I found your channel /cry

[@arjay_2002]

i see khanacademy more for high school students

[@markusdescheneaux5986]

@@arjay_2002 Nah I'm high school and this guy explains it so much more concisely and quickly

[@malithjayalath6417]

Very helpful explanation thank you❤

[@abdulrahmanmohamed4131]

Great as usual!!

[@abdiwarithwonwaka7345]

I want to thank u 🙏🏽🙏🏽 u save my degree from first semester thanks 🙏🏽

[@majestic7768]

Very nicely explained.

[@eddycriollo5556]

you deserve the world

[@Chelsea2009FC]

Very relaxing voice to listen to in the background while studying

[@user-cu4bf4gw8d]

Bro you are doing a good work

[@ahmedgad9400]

bro u are litteraly life changing and im still in week 2 in the college

[@botainalilangan8102]

Fantastic! Thanks :)

[@justinswag3403]

Love ur vids

[@KiranAshraf-pf6zt]

Your explanation is too good i m speechless here ❤ love from pakistan

[@obww306]

thanks sir, you are helping well :)

[@aurumyt223]

What software do you use for the calculations? Please let me know.

[@mehedihm]

Thank you

[@ella_lovelife9641]

I like the course it is so helpful, i can't understand my professor at all. Thank you so much.

[@finleypetit5197]

this guy is 10x better than my hack of a professor

[@negarfarahbakhsh4890]

thank you

[@uditsaxena3844]

awesome

[@uwamahoroisabelle4678]

What can you do if you have the decimal..

[@selmancelik9335]

İ think it must be f(7) instead of f(6) the midpoints are 1 3 5 7 great video dude and i have a question if we are dividing areas for rectangulars why we cant find error at linear functions like ax+b . On the book error func. is f'' h cube divide 3 . i mean for x square we have (2. H cube divide 3) error

[@WarriorAjk]

Yep he made a mistake there.

[@ItsLexrr]

Dr why isn't the number of terms 5 in the first example ? doesn't zero count as a term of "n" because from 0 and you divided to 3 points thats 4 and with the 8 thats 5 if you know what i mean, so could u please explain this point to me

[@isabellarestrepo5698]

Why was n replaced by 4 in the beginning? How do you know?

[@Beaumains314]

n is the number of sub intervals

[@neutronzz3543]

basically you can choose how many rectangles if you want less then it wont be as good of an approx, more rectangles will come closer to the exact answer and an infinite amount will give u the exact answer.

[@magicicicle2504]

thank you, you saved my grade

[@voltycclipz8384]

what if not given any subdivisions, how would u create a formula without using n instead of actual subdivisions

[@yunyung]

Without using n, you can technically use the usual integrating technique so as long as you have the a and b and function of the graph. In this video, he's just showcasing how to calculate for the area using Riemann sums (finding the area of the graph by using the sum of areas of rectangles)

[@simonpangan7470]

How do you get the "n" and what is the "n" represent?

[@monishaav5411]

n is the 4 sub intervals which is equally divided

[@willbutcher5083]

The ad goes like are the videos from 2006 really helping ? My answer: yes they are

[@josefurlan7999]

I love math classes

[@anthonytakouam2392]

Why can't professors explain this this well? Smh. 🙄🙄🤦‍♂️

[@sarahlolo2100]

Are these all calculus 1 videos? Please answer

[@alialden1258]

Calc 2 intro

[@jacquescoury2979]

well im learning this in calc 1 but i mean everything you learn you use it for future lessons and stuff so its applicable to calc 2 even more so, idk why it matters tho...

[@jesusquinonez3628]

How do I calculate n ?

[@zambotwu]

By now you prolly figured it out but for the sake of the other people, you decide how many rectangles you may want to use. The larger the number although tedious, the better approximation.

[@stuxx8843]

0:54 why is n=4??

[@yunyung]

He mentioned "We're gonna break it into 4 sub intervals" meaning for his given example, he decided to give it 4 subdivisions. Hence, n=4

[@allzpark]

i love u

[@lucasisasi9759]

How u got the “n”?

[@nexon7610]

The sub intervals or # of rectangles is how you get n

[@WarriorAjk]

At 4:56 they accidently write f(6) instead of f(7). They do fix it later on, but yeah don't get worried, f(7) is correct.

[@ratandeep6694]

We should all drop the concept of college and line up in front of you.

[@FelixBama-ky1ew]

He is

[@swamiyoda8926]

First comment again😆😆😆😆😆

[@Maniimula]

what is n ?

[@monishaav5411]

n is the 4 sub intervals which is equally divided

[@selulekotsabedze9137]

The number of intervals you wanna make under the graph, note the larger n is, the more accurate your approximation is.

[@mariamabdelatef5193]

bruh i should pay you my college tuition

[@xJinzoh]

what if b-a=0???

[@osama9659]

Its fine because that means the interval has no area

[@xJinzoh]

Sleepiest Six so it becomes an indefinite integral? lol or does the function become non-integratable

[@ashantinyongo7632]

It means it’s a point bruh

[@jackwells7482]

Why you got a perpetual cold

[@user-bt8nh4ou1p]

babyyyy girl whats yoiur name... lemme talk to you lemme buy you a drank... im T pain

[@fallingpotato9221]

as useful as this video is for finding approximations, he forgot to apply the limit as n approaches infinity to get the actual Reimann sum. To find the actual answer you just used the fundamental theorem of calculus. when you combine this with the limits and the summation formulas, then you will actually get a Reimann sum.

[@KiranAshraf-pf6zt]

Your explanation is too good i m speechless here ❤ love from pakistan