Finding The Area Using The Limit Definition & Sigma Notation

This calculus video tutorial explains how to find the area using the limit definition with sigma notation and summation formulas.
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...
__________________________________
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www.video-tutor.net/
Full-Length Videos and Worksheets:
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[@TheOrganicChemistryTutor]

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

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[@andrewmorgan3100]

After using all these steps: He says: "Now we apply math"

[@fryPS]

Should have said algebra

[@nicksacco5041]

Imagine having to use that limit definition for every problem

[@MagnusTheGreat]

That would suck.

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I would bleach out my eyeballs and then down the rest of the canister

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Lol. That would be child labour

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the more you do it the faster you get at it

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Integrating is easily the preferred method every time.

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[@usctrojanfreak]

My exam on this is tmrw and I''m studying it right now currently 3am :D

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@@cappuccino2901 got a 78 lol

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I thought I was gonna be stuck forever. KhanAcademt doesn't even have one of these videos. Thank you, OCT.

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they have an entire course on their website

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[@bellabiferali5278]

I thought this was so hard but you made it so easy!!! THANK YOU !!!

[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for showing How to find the Area using the Limit Definition and Sigma Notation in Calculus One. This old fashion method increases my understanding of the Summation Formulas and its impact on finding Areas under a curve. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

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you are the only one who gives the best intuition of integral calculus

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Thank you so much for this video! my calculus teacher should watch your videos so that he doe snot over complicate such an interesting and fun part of math that is integration.

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[@warwick802]

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[@danielbrown4031]

You make very clear instructional math videos, Mark Wahlberg. Thank you. But what is the difference between a and i, on here they are both 1, why have two different variables?

[@aintfalco7968]

who knew Marky Mark was such a math wiz

[@zepeterinma]

a is a constant representative of the beginning point on a graph holding the lowest x value. i is an iterator representing the integral between iterations and holds the temporary value of each point between a and b. [x2 - x1, y2 - y1] you use this, to find the difference between values of x and y as i goes up, the change in values between intervals is called delta. every time i goes up, the delta is added or subtracted to/from the previous value, for the total value adding up to y2. by finding the delta of both x and y per iteration, we are able to find the slope of the line (rise over run, or deltaY over deltaX), and we essentially get a right triangle in each iteration. The formula for finding the area of a right triangle is 1/2 base times height, or half delta x * y. We then add the area from each iteration to the sum of the areas of all the previous iterations to get the total area. If the mathematical way of doing this is difficult, you can also do this programmatically with a for loop. I am scared of watching the next videos though cuz i think im going to get lost soon. lmao

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When we are doing a laboration about synthesis of paracetamol and then analyzing It with TLC and melting point. What can we learn us afterwards?

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[@aghasabir6105]

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[@lactran2979]

Can you show some of the exercises or references related to this topic? Thank you, sir.

[@engmohan87]

Thankz pro......

[@mohanapriya1674]

excellent sir

[@aeriskabkr1110]

after understanding this theorem about calculating plane areas, I realized that the other topics like solids of revolution in which we compute volumes, finding the centroids and finding moment of inertia also follow the theorem being explain in the video,, the limit of the summation of rectangles as the number of rectangles approach infinity, it's width delta x approaches zero

[@user-fm1xl6sm5l]

Thanks!

[@mehedihm]

Very helpful

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[@umairfarooq7557]

Have you supposed value of n=4 or it is given?

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[@esthertesfai9559]

THANK YOU

[@luvdy7770]

how did you get the value that corresponds to the summation of i^3 to be n^2(n+1)^2/4

[@abhijeet_ghosh]

He uses summation rules, which you can learn online. He even has a video on summation rules: kzbin.info/www/bejne/jnvOepStZ8pkhtk

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Saved me again bro

[@SM-qn7sr]

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Thanks

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amazing video as always, but its hard to see the blue color could you use a color closer to cyan please

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Where did the stuff at 9:43 come from?

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an absolute god

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Can you also upload videos on programming

[@Ozzel1980]

Cramming the night before the AP calculus test...

[@blackholesun4942]

Thanks you

[@hakachukai]

Where did that term @9:39 come from? How does i^3 magically turn into [ n^2(n*1)^2 ] / 4 ???

[@person-fu1ex]

it is a formula that must be memorized

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"in this video" im pavloved to destress with that

[@maroonhorizon1693]

Ily 🤟🏾

[@pmcpreston]

How do you get formula for i? I cant find an answer anywhere.

[@selinabolella5553]

they're formulas you have to memorize for: i, i^2, and i^3. They're on google.

[@AnjuSingh-vm8wy]

God bless you

[@hassanalobud3817]

i really dont understand how im supposed to understand this in highschool

[@hassanalobud3817]

i mean i can get it but how am i gonna write all of these sympols and stuff

[@zahlen_0092]

@@hassanalobud3817 wish I got this in high school, avoided STEM in high school, ended up going to an engineering course in college and not knowing a lick of calculus is giving me a hard time lol

[@aminelkasaby1021]

@@zahlen_0092 I am going through the same situation too

[@hitopsful]

@@zahlen_0092 same bro

[@nahiansharif4200]

this is college stuff. u probably took high level class?

[@whymyruffles]

i remember when math used to have numbers.... lol

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I pay $16 a month for chegg study only for this to exist and be better :(

[@cathywillies1927]

This is what they'll give to solve for 1 minutes in exam. I was unable to think 😪🤧

[@jalvarez8626]

this is the most annoying part about calculus. once I got to learning about the fundamental theory calculus, every time I did a limit problem I did the biggest eye-roll ever

[@amruthadhanabalan1328]

Cooooooooooooolllllll

[@mercyymene]

I’ve been enjoying all of the other videos and now there’s this one… area in calculus again I’m so confused and stuck here 😭💔

[@matts2565]

Same here I'm with you we will conquer this BS lol

[@Nada4_9]

For the first time, I cannot understand what you are saying, and I am sure that the problem is with me

[@serinacat4781]

These saves my ass

[@xk3113]

This topic is hard

[@yasmeenkarachiwala9612]

Why is n constant?

[@tansy2279]

n doesnt change value, and therefore is a constant and can be treated as such

[@user-kn2ub2cj8z]

💛💛💛

[@matts2565]

God this section sucks so much. Thank you sm as always you are a lifesaver

[@user-wk4jm9sp1z]

3:03 why n=4?

[@user-ch6xl1zc6k]

It’s arbitrary, 4 is easy to demonstrate quickly. n can be chosen, and the bigger n is the more precise the calculation

[@Sunita_Notiyal]

Mississippi

[@user-kn2ub2cj8z]

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Are you an angel?

[@user-kn2ub2cj8z]

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[@toi_let954]

The limit definition is so tedious and annoying to do, thank god for shortcuts and stuff.

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i fucking love you

[@user-kn2ub2cj8z]

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[@siryogi1563]

Good video but how is this suppose to help me pay my car bill again ?

[@GamerTheTurtle]

because you need that A in all three of your calculus classes to become get your undergrad then get your nice six figure job. if you're not pursuing a STEM course what the fuck are you watching this video for? LOL

[@tansy2279]

@@GamerTheTurtle is calculus only for stem?

[@juandiegomoreno9803]

@@tansy2279 not exclusively, but calculus is most relevant to STEM fields

[@brandonmtb3767]

Why would you wanna do so much work when you can use the integral

[@fryPS]

Right!? I'm assuming there's a good reason to use this unless they just don't want future generations to forget this method for some reason.

[@sohamsantra7548]

This channel should be renamed to Grade saving tutor!

[@kkaeru]

im definetely not passing my final lmfao

[@abinjohn8133]

Dark blue is a little too dark

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Seems pretty bright to me

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شريف

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Am i the only one who got this for 8th grade HW and dont know WTF is going on

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bro i will get a 100 for you

[@violethill4454]

i prefer professor leonard's lesson on this one: kzbin.info/www/bejne/gWGyg3d5qZp8nZI

[@lucyferguson9020]

made absolutely no sense but that's probably because i'm stupid and shouldn't have taken maths alevel

[@mac2857]

all that just to integrate in the end should've started with that smh wasted 13 minutes

[@bertnycaller1705]

Hey! Why is the i is written as a subscript, but you are having the multiply when done? female dog

[@user-kn2ub2cj8z]

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