Midpoint Rule & Riemann Sums

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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:

Basic Integration Problems:

Indefinite Integral:

Definite Integral:

Differential Equations:

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Properties of Definite Integrals:

Rectilinear Motion Problems:

Sigma Notation - Calculus:

Riemann Sums - Area:

The Midpoint Rule:

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Finding Area - Limit Definition:

Definite Integrals - Geometry:

Fundamental Theorem - Part 1:

Fundamental Theorem - Part 2:

Net Change Theorem:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:
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My Guy you literally saving my degree here

danielukpe
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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! ❤️❤️❤️

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

rubenrenteria
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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 YouTube TV with the Organic Chemistry Tutor.

georgesadler
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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.

anicredible
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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!

euclid
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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.

chriswilliams
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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. 😊

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

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

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

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

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

jeremyhopkins
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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.

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

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

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

KiranAshraf-pfzt
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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

selmancelik
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Very relaxing voice to listen to in the background while studying

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

isabellarestrepo