Finding The Area Using The Limit Definition & Sigma Notation

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  • Опубликовано: 30 ноя 2024

Комментарии • 163

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Год назад +9

    Applications of Integration - Free Formula Sheet: bit.ly/3ZdKSnK
    Next Video: ruclips.net/video/ghxEOz9rmwE/видео.html

  • @madboycal7859
    @madboycal7859 3 года назад +333

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

    • @La_ndon
      @La_ndon Год назад +1

      Istg

    • @sotruemrcat
      @sotruemrcat 6 месяцев назад +1

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

  • @alygoldsborough1857
    @alygoldsborough1857 10 месяцев назад +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 лет назад +168

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

  • @DomenicC-e3u
    @DomenicC-e3u 2 месяца назад +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 лет назад +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 года назад +4

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

    • @dragonllig790
      @dragonllig790 4 года назад +2

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

    • @usctrojanfreak
      @usctrojanfreak 4 года назад +4

      @@dragonllig790 study then man! lol

    • @cappuccino2901
      @cappuccino2901 3 года назад +2

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

    • @usctrojanfreak
      @usctrojanfreak 3 года назад +5

      @@cappuccino2901 got a 78 lol

  • @kingpamz
    @kingpamz 4 года назад +140

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

  • @aliaisaacs6591
    @aliaisaacs6591 4 года назад +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 !

  • @hussainn.al-saeed4971
    @hussainn.al-saeed4971 4 года назад +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

  • @Trynnagetmydegree__
    @Trynnagetmydegree__ Год назад +5

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

  • @nicksacco5041
    @nicksacco5041 6 лет назад +411

    Imagine having to use that limit definition for every problem

    • @MagnusTheGreat
      @MagnusTheGreat 6 лет назад +21

      That would suck.

    • @redtrek1239
      @redtrek1239 4 года назад +50

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

    • @tomatrix7525
      @tomatrix7525 4 года назад +2

      Lol. That would be child labour

    • @healthware
      @healthware 4 года назад +11

      the more you do it the faster you get at it

    • @warwick802
      @warwick802 2 года назад +10

      Integrating is easily the preferred method every time.

  • @onebunnehenry5335
    @onebunnehenry5335 3 года назад +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 Год назад

      Which type of engineering r you

    • @onebunnehenry5335
      @onebunnehenry5335 Год назад +2

      @@bountiful14 Mechanical Engineering

    • @bountiful14
      @bountiful14 Год назад

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

    • @cozz124
      @cozz124 12 дней назад

      there is no god here

  • @rafeeqmuhammad4332
    @rafeeqmuhammad4332 5 лет назад +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 года назад

      they have an entire course on their website

  • @ayshaghanawi9941
    @ayshaghanawi9941 2 года назад +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 Год назад +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 RUclips TV with the Organic Chemistry Tutor.

  • @andrewmorgan3100
    @andrewmorgan3100 4 года назад +72

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

    • @fryPS
      @fryPS 3 года назад

      Should have said algebra

  • @Mulla-alyusufi
    @Mulla-alyusufi Год назад

    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 лет назад +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 года назад

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

  • @danielbrown4031
    @danielbrown4031 6 лет назад +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 лет назад +7

      who knew Marky Mark was such a math wiz

    • @zepeterinma
      @zepeterinma 3 года назад +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 года назад

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

  • @nhanhuynh4834
    @nhanhuynh4834 4 года назад +1

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

  • @warwick802
    @warwick802 2 года назад +9

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

    • @Jen_046
      @Jen_046 Год назад

      you go to uni of warwick bro ? 😂😂

  • @bellabiferali5278
    @bellabiferali5278 4 года назад +4

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

  • @JoeMama-bo6di
    @JoeMama-bo6di 16 дней назад +3

    who else is watching this 30 minutes before their test?

  • @aeriskabkr1110
    @aeriskabkr1110 8 месяцев назад

    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 года назад +2

    YOU THE BEST AND THE BEAST MAN

  • @HitmanThunder
    @HitmanThunder 6 лет назад +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 лет назад

    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.

  • @004klllllll
    @004klllllll 11 месяцев назад +5

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

    • @omajith2372
      @omajith2372 2 месяца назад

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

  • @travisj5736
    @travisj5736 4 года назад +4

    Bro you are carrying me thru online school

  • @blepblop8213
    @blepblop8213 3 года назад

    YOU ARE SUCH A HERO

  • @luvdy7770
    @luvdy7770 4 года назад +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 года назад +2

      He uses summation rules, which you can learn online. He even has a video on summation rules: ruclips.net/video/XJkIaw2e1Pw/видео.html

  • @OpLapDancePikachu69
    @OpLapDancePikachu69 10 месяцев назад +1

    "in this video" im pavloved to destress with that

  • @lactran2979
    @lactran2979 7 месяцев назад

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

  • @SM-qn7sr
    @SM-qn7sr 2 года назад

    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 года назад +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 лет назад

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

  • @AuraRazor
    @AuraRazor 5 лет назад

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

  • @gabrielrodriguez6501
    @gabrielrodriguez6501 Месяц назад

    You’re actually a god

  • @manicjupiterflute
    @manicjupiterflute Год назад +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 года назад

    I am giving you standing ovations.

  • @Good-xc7qh
    @Good-xc7qh 3 года назад +1

    Thanks

  • @Ozzel1980
    @Ozzel1980 2 года назад

    Cramming the night before the AP calculus test...

  • @PotatoBoiOfficial
    @PotatoBoiOfficial Год назад

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

  • @abrarmahi
    @abrarmahi 5 лет назад +2

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

  • @linneaandersson4163
    @linneaandersson4163 6 лет назад

    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 месяца назад

    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 лет назад +25

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

    • @hassanalobud3817
      @hassanalobud3817 6 лет назад +3

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

    • @zahlen_0092
      @zahlen_0092 5 лет назад +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 лет назад

      @@zahlen_0092 I am going through the same situation too

    • @hitopsful
      @hitopsful 4 года назад

      @@zahlen_0092 same bro

    • @nahiansharif4200
      @nahiansharif4200 4 года назад

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

  • @aghasabir6105
    @aghasabir6105 4 года назад

    Thanx a lot I have cleared 👍

  • @hakachukai
    @hakachukai 3 года назад +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 года назад +1

      it is a formula that must be memorized

  • @kevinsnaterse4692
    @kevinsnaterse4692 3 года назад

    Saved me again bro

  • @skizakapiye9510
    @skizakapiye9510 2 года назад

    You're the man

  • @mercyymene
    @mercyymene 3 года назад +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 года назад +1

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

  • @sa21456
    @sa21456 4 года назад

    You are my hero

  • @mohanapriya1674
    @mohanapriya1674 4 года назад

    excellent sir

  • @Jawahir-l5u
    @Jawahir-l5u 2 года назад

    Thank you

  • @angelreyes4381
    @angelreyes4381 4 года назад

    an absolute god

  • @esthertesfai9559
    @esthertesfai9559 4 года назад

    THANK YOU

  • @engmohan87
    @engmohan87 5 лет назад +2

    Thankz pro......

  • @mehedihm
    @mehedihm 4 года назад

    Very helpful

  • @cathywillies1927
    @cathywillies1927 8 месяцев назад

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

  • @umairfarooq7557
    @umairfarooq7557 3 года назад

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

  • @Hassan_X_Israr
    @Hassan_X_Israr Год назад

    Can you also upload videos on programming

  • @niyonsabaTreasure
    @niyonsabaTreasure 10 месяцев назад

    Thanks alot sir🙏🥹

  • @GiftMlinde
    @GiftMlinde Месяц назад

    Thenks sir!

  • @whymyruffles
    @whymyruffles 2 года назад +1

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

  • @toi_let954
    @toi_let954 3 года назад

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

  • @nandimnguni2216
    @nandimnguni2216 4 месяца назад

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

    • @GD_Anchanix
      @GD_Anchanix Месяц назад

      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 года назад

    Where did the stuff at 9:43 come from?

  • @danielcervini2545
    @danielcervini2545 2 года назад

    Are you an angel?

  • @brandonmtb3767
    @brandonmtb3767 4 года назад +2

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

    • @fryPS
      @fryPS 3 года назад +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.

  • @blackholesun4942
    @blackholesun4942 8 месяцев назад

    Thanks you

  • @alisonpasquarette5909
    @alisonpasquarette5909 Месяц назад

    How did you get 4096?

  • @AnjuSingh-vm8wy
    @AnjuSingh-vm8wy Год назад

    God bless you

  • @pmcpreston
    @pmcpreston 4 года назад

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

    • @selinabolella5553
      @selinabolella5553 4 года назад

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

  • @matts2565
    @matts2565 3 года назад

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

  • @siryogi1563
    @siryogi1563 6 лет назад +36

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

    • @GamerTheTurtle
      @GamerTheTurtle 5 лет назад +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 года назад

      @@GamerTheTurtle is calculus only for stem?

    • @juandiegomoreno9803
      @juandiegomoreno9803 3 года назад

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

  • @maroonhorizon1693
    @maroonhorizon1693 5 лет назад +1

    Ily 🤟🏾

  • @xk3113
    @xk3113 4 года назад +1

    This topic is hard

  • @sohamsantra7548
    @sohamsantra7548 3 года назад

    This channel should be renamed to Grade saving tutor!

  • @yasmeenkarachiwala9612
    @yasmeenkarachiwala9612 4 года назад

    Why is n constant?

    • @tansy2279
      @tansy2279 4 года назад

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

  • @Sunita_Notiyal
    @Sunita_Notiyal Год назад

    Mississippi

  • @彥宇-o5c
    @彥宇-o5c Год назад

    3:03 why n=4?

    • @user-ch6xl1zc6k
      @user-ch6xl1zc6k Год назад

      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 года назад +1

    These saves my ass

  • @abinjohn8133
    @abinjohn8133 4 года назад

    Dark blue is a little too dark

    • @tansy2279
      @tansy2279 4 года назад

      Seems pretty bright to me

  • @kkaeru
    @kkaeru 3 года назад

    im definetely not passing my final lmfao

  • @divineaxel9764
    @divineaxel9764 4 года назад

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

  • @Jawahir-l5u
    @Jawahir-l5u 2 года назад

    💛💛💛

  • @amruthadhanabalan1328
    @amruthadhanabalan1328 6 лет назад +2

    Cooooooooooooolllllll

  • @Jawahir-l5u
    @Jawahir-l5u 2 года назад

    💛💛💛💛

  • @omegabowl6857
    @omegabowl6857 5 лет назад

    i fucking love you

  • @lucyferguson9020
    @lucyferguson9020 3 года назад

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

  • @goksuphysics
    @goksuphysics 6 месяцев назад

    bro i will get a 100 for you

  • @Jawahir-l5u
    @Jawahir-l5u 2 года назад

    💛💛💛💛💛💛💛💛

  • @JafarAl-Habib
    @JafarAl-Habib 2 года назад

    شريف

  • @violethill4454
    @violethill4454 11 месяцев назад

    i prefer professor leonard's lesson on this one: ruclips.net/video/K0ORDCt5Ig0/видео.html

  • @mac2857
    @mac2857 11 месяцев назад

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

  • @bertnycaller1705
    @bertnycaller1705 2 года назад

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