Finding The Area Using The Limit Definition & Sigma Notation

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  • Опубліковано 1 гру 2024

КОМЕНТАРІ • 163

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Рік тому +9

    Applications of Integration - Free Formula Sheet: bit.ly/3ZdKSnK
    Next Video: ua-cam.com/video/ghxEOz9rmwE/v-deo.html

  • @madboycal7859
    @madboycal7859 3 роки тому +333

    I'll say it again, this man deserves some of our tuition more than our professors.

    • @La_ndon
      @La_ndon Рік тому +1

      Istg

    • @sotruemrcat
      @sotruemrcat 6 місяців тому +1

      Trust me he gets more money from youtube views and subs so no worries 😂

  • @alygoldsborough1857
    @alygoldsborough1857 10 місяців тому +24

    I zone out in calc and miss a few classes from being sick, and you’ve caught me up in half of an hour. May God bless you abundantly, and I hope you know how much of a positive impact you make on so many student’s education!

  • @jeffreyma625
    @jeffreyma625 6 років тому +168

    This tutor is absolutely a genius!!! He posts video on every subjects!!!!

  • @DomenicC-e3u
    @DomenicC-e3u 2 місяці тому +13

    I find it funny how he does not usually respond to comments, his "out of the public eye" behaviour reminds me of a superhero who doesn't do it for the fame or for the glory, but for the people.

  • @theog6494
    @theog6494 5 років тому +44

    watching this at 1.30am with my assignment due tomorrow. You are a lifesaver. thank you for this (and your accent is fantastic)

    • @usctrojanfreak
      @usctrojanfreak 4 роки тому +4

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

    • @dragonllig790
      @dragonllig790 4 роки тому +2

      @@usctrojanfreak at least you studied god mine in a few days

    • @usctrojanfreak
      @usctrojanfreak 4 роки тому +4

      @@dragonllig790 study then man! lol

    • @cappuccino2901
      @cappuccino2901 3 роки тому +2

      @@usctrojanfreak how was ur exam? did you do well?

    • @usctrojanfreak
      @usctrojanfreak 3 роки тому +5

      @@cappuccino2901 got a 78 lol

  • @kingpamz
    @kingpamz 4 роки тому +140

    I literally watched all the ads in this video because its the least I can do to thank him

  • @aliaisaacs6591
    @aliaisaacs6591 4 роки тому +19

    Content creator, whoever you may be, thank you from the bottom of heart!! Sending love and gratitude as a first year South African Engineering Student !

  • @Trynnagetmydegree__
    @Trynnagetmydegree__ Рік тому +6

    Thank you again dude, I seriously owe it all to you for helping me understand this madness that professors oftentimes fail to explain.

  • @hussainn.al-saeed4971
    @hussainn.al-saeed4971 4 роки тому +23

    Man you saved my life in alot of things
    Every time I don’t know a thing i search for your videos especially because you are the only one who make it very clear and because all my teachers at college sucks especially in this time with the classroom thing
    You are a college to me
    Thank you very much

  • @nicksacco5041
    @nicksacco5041 6 років тому +411

    Imagine having to use that limit definition for every problem

    • @MagnusTheGreat
      @MagnusTheGreat 6 років тому +21

      That would suck.

    • @redtrek1239
      @redtrek1239 4 роки тому +50

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

    • @tomatrix7525
      @tomatrix7525 4 роки тому +2

      Lol. That would be child labour

    • @healthware
      @healthware 4 роки тому +11

      the more you do it the faster you get at it

    • @warwick802
      @warwick802 2 роки тому +10

      Integrating is easily the preferred method every time.

  • @onebunnehenry5335
    @onebunnehenry5335 3 роки тому +14

    As an engineer, learning calculus through you has always been a piece of cake........................Thank you so much The Organic Chemistry Tutor.

    • @bountiful14
      @bountiful14 Рік тому

      Which type of engineering r you

    • @onebunnehenry5335
      @onebunnehenry5335 Рік тому +2

      @@bountiful14 Mechanical Engineering

    • @bountiful14
      @bountiful14 Рік тому

      @@onebunnehenry5335 cool! Thats what i wanna study when i get to college. Whats it like

    • @cozz124
      @cozz124 13 днів тому

      there is no god here

  • @rafeeqmuhammad4332
    @rafeeqmuhammad4332 5 років тому +65

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

    • @dhiva-san
      @dhiva-san 4 роки тому

      they have an entire course on their website

  • @ayshaghanawi9941
    @ayshaghanawi9941 2 роки тому +3

    I'm so glad God led me to your videos. Whenever I'm confused about a certain topic I search for you. There was this one time where I had watched all the collegeboard vidoes but was still lost and then I decided to search for you. I spent the remaining 6 hours of my day watching your videos and was able to pass my exam. I'm so grateful you post these videos and you should know that God will reward you immensely for teaching us all this material when we are in a time of need.

  • @georgesadler7830
    @georgesadler7830 Рік тому +1

    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 UA-cam TV with the Organic Chemistry Tutor.

  • @andrewmorgan3100
    @andrewmorgan3100 4 роки тому +72

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

    • @fryPS
      @fryPS 3 роки тому

      Should have said algebra

  • @Mulla-alyusufi
    @Mulla-alyusufi Рік тому

    Thank you bro.
    I am searching any video that African boy. Who cant speak English .
    I understand you.
    I appreciate god will give you best thing. Insha allah.

  • @kainatnaqvi5319
    @kainatnaqvi5319 6 років тому +22

    Thank you so much man!
    I have been looking for such tutorial for months.. and now my final terms are just a week away and finalllllly i found this topic and you explained it very well...
    Thanks a bunch 👌👌👌👌

  • @dlwlrmae
    @dlwlrmae 3 роки тому

    you have no idea how much i owe you for all that you do

  • @danielbrown4031
    @danielbrown4031 6 років тому +71

    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
      @aintfalco7968 5 років тому +7

      who knew Marky Mark was such a math wiz

    • @zepeterinma
      @zepeterinma 3 роки тому +2

      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

  • @User-cc4lz
    @User-cc4lz 3 роки тому

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

  • @warwick802
    @warwick802 2 роки тому +9

    I just understood a 2 hour lecture in 13 minutes better than I did in class.

    • @Jen_046
      @Jen_046 Рік тому

      you go to uni of warwick bro ? 😂😂

  • @nhanhuynh4834
    @nhanhuynh4834 4 роки тому +1

    This video just save my life! Really appreciate your clear explanation!

  • @bellabiferali5278
    @bellabiferali5278 4 роки тому +4

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

  • @JoeMama-bo6di
    @JoeMama-bo6di 17 днів тому +3

    who else is watching this 30 minutes before their test?

  • @aeriskabkr1110
    @aeriskabkr1110 8 місяців тому

    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

  • @syabongajele6431
    @syabongajele6431 4 роки тому +2

    YOU THE BEST AND THE BEAST MAN

  • @004klllllll
    @004klllllll 11 місяців тому +6

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

    • @omajith2372
      @omajith2372 2 місяці тому

      He does something in there that you need a formula for that he doesn’t explain

  • @HitmanThunder
    @HitmanThunder 6 років тому +7

    Hey can I ask a quick question, what is the difference between the "Organic Chemistry Video Tutorial Playlist" and "Organic Chemistry New Playlist Online Video Tutorial Course"?

  • @ivancheems35
    @ivancheems35 5 років тому

    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.

  • @travisj5736
    @travisj5736 4 роки тому +4

    Bro you are carrying me thru online school

  • @blepblop8213
    @blepblop8213 3 роки тому

    YOU ARE SUCH A HERO

  • @luvdy7770
    @luvdy7770 4 роки тому +5

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

    • @abhijeet_ghosh
      @abhijeet_ghosh 2 роки тому +2

      He uses summation rules, which you can learn online. He even has a video on summation rules: ua-cam.com/video/XJkIaw2e1Pw/v-deo.html

  • @OpLapDancePikachu69
    @OpLapDancePikachu69 10 місяців тому +1

    "in this video" im pavloved to destress with that

  • @lactran2979
    @lactran2979 7 місяців тому

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

  • @SM-qn7sr
    @SM-qn7sr 2 роки тому

    I am so glad OCT has a tutorial for this. I am on this chapter and this is the first time I don’t get something right away

  • @jalvarez8626
    @jalvarez8626 2 роки тому +1

    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

  • @niloofarkheradmand9719
    @niloofarkheradmand9719 5 років тому

    It was very helpful!!!! thank you so much.

  • @AuraRazor
    @AuraRazor 5 років тому

    dude your a fucking g, you have a video for every lesson in my calc class

  • @gabrielrodriguez6501
    @gabrielrodriguez6501 Місяць тому

    You’re actually a god

  • @manicjupiterflute
    @manicjupiterflute Рік тому +1

    This guy has such a sexy voice. He sounds exactly like Mark Wahlberg. I could seriously listen to this guy talk about calculus all day.

  • @teymurasgarli9506
    @teymurasgarli9506 4 роки тому

    I am giving you standing ovations.

  • @Good-xc7qh
    @Good-xc7qh 3 роки тому +1

    Thanks

  • @Ozzel1980
    @Ozzel1980 2 роки тому

    Cramming the night before the AP calculus test...

  • @PotatoBoiOfficial
    @PotatoBoiOfficial Рік тому

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

  • @abrarmahi
    @abrarmahi 5 років тому +2

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

  • @linneaandersson4163
    @linneaandersson4163 6 років тому

    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?

  • @mayavictoria5462
    @mayavictoria5462 3 місяці тому

    I almost killed myself after two hours of trying to teach this to myself using my textbook and teachers notes. This might have saved my life, thankyou

  • @hassanalobud3817
    @hassanalobud3817 6 років тому +25

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

    • @hassanalobud3817
      @hassanalobud3817 6 років тому +3

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

    • @zahlen_0092
      @zahlen_0092 5 років тому +12

      @@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

    • @Cpt.Price123
      @Cpt.Price123 5 років тому

      @@zahlen_0092 I am going through the same situation too

    • @hitopsful
      @hitopsful 4 роки тому

      @@zahlen_0092 same bro

    • @nahiansharif4200
      @nahiansharif4200 4 роки тому

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

  • @hakachukai
    @hakachukai 3 роки тому +1

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

    • @person-fu1ex
      @person-fu1ex 3 роки тому +1

      it is a formula that must be memorized

  • @aghasabir6105
    @aghasabir6105 4 роки тому

    Thanx a lot I have cleared 👍

  • @kevinsnaterse4692
    @kevinsnaterse4692 3 роки тому

    Saved me again bro

  • @skizakapiye9510
    @skizakapiye9510 2 роки тому

    You're the man

  • @mercyymene
    @mercyymene 3 роки тому +1

    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
      @matts2565 3 роки тому +1

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

  • @sa21456
    @sa21456 4 роки тому

    You are my hero

  • @mohanapriya1674
    @mohanapriya1674 4 роки тому

    excellent sir

  • @Jawahir-l5u
    @Jawahir-l5u 2 роки тому

    Thank you

  • @angelreyes4381
    @angelreyes4381 4 роки тому

    an absolute god

  • @esthertesfai9559
    @esthertesfai9559 4 роки тому

    THANK YOU

  • @engmohan87
    @engmohan87 5 років тому +2

    Thankz pro......

  • @mehedihm
    @mehedihm 4 роки тому

    Very helpful

  • @cathywillies1927
    @cathywillies1927 8 місяців тому

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

  • @umairfarooq7557
    @umairfarooq7557 3 роки тому

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

  • @Hassan_X_Israr
    @Hassan_X_Israr Рік тому

    Can you also upload videos on programming

  • @niyonsabaTreasure
    @niyonsabaTreasure 10 місяців тому

    Thanks alot sir🙏🥹

  • @GiftMlinde
    @GiftMlinde Місяць тому

    Thenks sir!

  • @whymyruffles
    @whymyruffles 2 роки тому +1

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

  • @toi_let954
    @toi_let954 3 роки тому

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

  • @nandimnguni2216
    @nandimnguni2216 4 місяці тому

    11:01 why are we multiplying by 1/n^2 ?

    • @GD_Anchanix
      @GD_Anchanix Місяць тому

      i think its to remove the denominator, even still just that last bit where the guy evaluates his answer will probably give you all the marks and save loads of time and brainpower to also

  • @neuronoc.7343
    @neuronoc.7343 3 роки тому

    Where did the stuff at 9:43 come from?

  • @danielcervini2545
    @danielcervini2545 2 роки тому

    Are you an angel?

  • @brandonmtb3767
    @brandonmtb3767 4 роки тому +2

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

    • @fryPS
      @fryPS 3 роки тому +1

      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.

  • @alisonpasquarette5909
    @alisonpasquarette5909 Місяць тому

    How did you get 4096?

  • @blackholesun4942
    @blackholesun4942 8 місяців тому

    Thanks you

  • @AnjuSingh-vm8wy
    @AnjuSingh-vm8wy Рік тому

    God bless you

  • @pmcpreston
    @pmcpreston 4 роки тому

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

    • @selinabolella5553
      @selinabolella5553 4 роки тому

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

  • @matts2565
    @matts2565 3 роки тому

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

  • @siryogi1563
    @siryogi1563 6 років тому +36

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

    • @GamerTheTurtle
      @GamerTheTurtle 5 років тому +11

      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
      @tansy2279 4 роки тому

      @@GamerTheTurtle is calculus only for stem?

    • @juandiegomoreno9803
      @juandiegomoreno9803 3 роки тому

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

  • @maroonhorizon1693
    @maroonhorizon1693 5 років тому +1

    Ily 🤟🏾

  • @xk3113
    @xk3113 4 роки тому +1

    This topic is hard

  • @sohamsantra7548
    @sohamsantra7548 3 роки тому

    This channel should be renamed to Grade saving tutor!

  • @yasmeenkarachiwala9612
    @yasmeenkarachiwala9612 4 роки тому

    Why is n constant?

    • @tansy2279
      @tansy2279 4 роки тому

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

  • @Sunita_Notiyal
    @Sunita_Notiyal Рік тому

    Mississippi

  • @彥宇-o5c
    @彥宇-o5c Рік тому

    3:03 why n=4?

    • @user-ch6xl1zc6k
      @user-ch6xl1zc6k Рік тому

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

  • @serinacat4781
    @serinacat4781 4 роки тому +1

    These saves my ass

  • @abinjohn8133
    @abinjohn8133 4 роки тому

    Dark blue is a little too dark

    • @tansy2279
      @tansy2279 4 роки тому

      Seems pretty bright to me

  • @kkaeru
    @kkaeru 3 роки тому

    im definetely not passing my final lmfao

  • @divineaxel9764
    @divineaxel9764 4 роки тому

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

  • @Jawahir-l5u
    @Jawahir-l5u 2 роки тому

    💛💛💛

  • @amruthadhanabalan1328
    @amruthadhanabalan1328 6 років тому +2

    Cooooooooooooolllllll

  • @Jawahir-l5u
    @Jawahir-l5u 2 роки тому

    💛💛💛💛

  • @omegabowl6857
    @omegabowl6857 5 років тому

    i fucking love you

  • @lucyferguson9020
    @lucyferguson9020 3 роки тому

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

  • @goksuphysics
    @goksuphysics 6 місяців тому

    bro i will get a 100 for you

  • @Jawahir-l5u
    @Jawahir-l5u 2 роки тому

    💛💛💛💛💛💛💛💛

  • @JafarAl-Habib
    @JafarAl-Habib 2 роки тому

    شريف

  • @violethill4454
    @violethill4454 11 місяців тому

    i prefer professor leonard's lesson on this one: ua-cam.com/video/K0ORDCt5Ig0/v-deo.html

  • @mac2857
    @mac2857 11 місяців тому

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

  • @bertnycaller1705
    @bertnycaller1705 2 роки тому

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