Finding The Area Using The Limit Definition & Sigma Notation

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  • Опубликовано: 12 янв 2025

Комментарии • 169

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Год назад +10

    Applications of Integration - Free Formula Sheet: bit.ly/3ZdKSnK
    Calculus 1 Final Exam Review: ruclips.net/video/WmBzmHru78w/видео.html
    Next Video: ruclips.net/video/ghxEOz9rmwE/видео.html

  • @madboycal7859
    @madboycal7859 3 года назад +358

    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 7 месяцев назад +2

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

  • @alygoldsborough1857
    @alygoldsborough1857 11 месяцев назад +32

    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 +170

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

  • @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)

    • @BrotherIntel
      @BrotherIntel 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

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

    • @BrotherIntel
      @BrotherIntel 4 года назад +4

      @@dragonllig790 study then man! lol

    • @cappuccino2901
      @cappuccino2901 4 года назад +3

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

    • @BrotherIntel
      @BrotherIntel 4 года назад +5

      @@cappuccino2901 got a 78 lol

  • @DomenicC-e3u
    @DomenicC-e3u 4 месяца назад +32

    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.

    • @teemomain330
      @teemomain330 12 дней назад

      There's too many comments to respond to.

  • @kingpamz
    @kingpamz 4 года назад +143

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

  • @Trynnagetmydegree__
    @Trynnagetmydegree__ Год назад +7

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

  • @aliaisaacs6591
    @aliaisaacs6591 4 года назад +20

    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

  • @nicksacco5041
    @nicksacco5041 6 лет назад +422

    Imagine having to use that limit definition for every problem

    • @MagnusTheGreat
      @MagnusTheGreat 6 лет назад +21

      That would suck.

    • @redtrek1239
      @redtrek1239 4 года назад +51

      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 +11

      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 Месяц назад

      there is no god here

    • @sebby2847
      @sebby2847 Месяц назад

      @@cozz124 LOLLL reading this while studying for my calc final on monday 😭

  • @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

  • @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

  • @ayshaghanawi9941
    @ayshaghanawi9941 3 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.

  • @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 👌👌👌👌

  • @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.

  • @dlwlrmaeve
    @dlwlrmaeve 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 +3

      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

  • @bellabiferali5278
    @bellabiferali5278 4 года назад +4

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

  • @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 ? 😂😂

  • @nhanhuynh4834
    @nhanhuynh4834 4 года назад +1

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

  • @JoeMama-bo6di
    @JoeMama-bo6di Месяц назад +4

    who else is watching this 30 minutes before their test?

  • @travisj5736
    @travisj5736 4 года назад +4

    Bro you are carrying me thru online school

  • @syabongajele6431
    @syabongajele6431 4 года назад +2

    YOU THE BEST AND THE BEAST MAN

  • @SM-qn7sr
    @SM-qn7sr 2 года назад +1

    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

  • @Ahmetİçöz-y3d
    @Ahmetİçöz-y3d 25 дней назад

    you are the king lives with us

  • @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.

  • @aeriskabkr1110
    @aeriskabkr1110 9 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

  • @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"?

  • @AuraRazor
    @AuraRazor 5 лет назад +1

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

  • @OpLapDancePikachu69
    @OpLapDancePikachu69 Год назад +1

    "in this video" im pavloved to destress with that

  • @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

  • @004klllllll
    @004klllllll Год назад +7

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

    • @omajith2372
      @omajith2372 3 месяца назад

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

  • @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

  • @blepblop8213
    @blepblop8213 3 года назад

    YOU ARE SUCH A HERO

  • @teymurasgarli9506
    @teymurasgarli9506 4 года назад

    I am giving you standing ovations.

  • @gabrielrodriguez6501
    @gabrielrodriguez6501 2 месяца назад

    You’re actually a god

  • @Mako_Abraham.N
    @Mako_Abraham.N 27 дней назад

    Thank you so much sir❤️

  • @niloofarkheradmand9719
    @niloofarkheradmand9719 5 лет назад

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

  • @lactran2979
    @lactran2979 8 месяцев назад

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

  • @aghasabir6105
    @aghasabir6105 4 года назад

    Thanx a lot I have cleared 👍

  • @Ozzel1980
    @Ozzel1980 2 года назад

    Cramming the night before the AP calculus test...

  • @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.

  • @g17asahandle
    @g17asahandle 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

  • @neuronoc.7343
    @neuronoc.7343 3 года назад

    Where did the stuff at 9:43 come from?

  • @mayavictoria5462
    @mayavictoria5462 5 месяцев 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

  • @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?

  • @nandimnguni2216
    @nandimnguni2216 5 месяцев назад

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

    • @Anchanix_RioClic666
      @Anchanix_RioClic666 2 месяца 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

  • @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?

  • @abrarmahi
    @abrarmahi 5 лет назад +2

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

  • @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

  • @cathywillies1927
    @cathywillies1927 10 месяцев назад

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

  • @kevinsnaterse4692
    @kevinsnaterse4692 3 года назад

    Saved me again bro

  • @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

  • @mohanapriya1674
    @mohanapriya1674 5 лет назад

    excellent sir

  • @0xAbuAli
    @0xAbuAli 2 года назад +1

    Thanks!

  • @sa21456
    @sa21456 4 года назад

    You are my hero

  • @angelreyes4381
    @angelreyes4381 4 года назад

    an absolute god

  • @skizakapiye9510
    @skizakapiye9510 2 года назад

    You're the man

  • @engmohan87
    @engmohan87 5 лет назад +2

    Thankz pro......

  • @mehedihm
    @mehedihm 4 года назад

    Very helpful

  • @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 +2

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

  • @whymyruffles
    @whymyruffles 2 года назад +1

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

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

    Thanks

  • @esthertesfai9559
    @esthertesfai9559 4 года назад

    THANK YOU

  • @niyonsabaTreasure
    @niyonsabaTreasure 11 месяцев назад

    Thanks alot sir🙏🥹

  • @彥宇-o5c
    @彥宇-o5c 2 года 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

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

    Thank you

  • @toi_let954
    @toi_let954 3 года назад

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

  • @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 +12

      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 +1

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

    • @GHOSTFACEKILLAv2
      @GHOSTFACEKILLAv2 25 дней назад +1

      Engineering 🙌

  • @alisonpasquarette5909
    @alisonpasquarette5909 2 месяца назад

    How did you get 4096?

  • @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.

  • @maroonhorizon1693
    @maroonhorizon1693 5 лет назад +1

    Ily 🤟🏾

  • @matts2565
    @matts2565 3 года назад

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

  • @GiftMlinde
    @GiftMlinde 3 месяца назад

    Thenks sir!

  • @kkaeru
    @kkaeru 3 года назад

    im definetely not passing my final lmfao

  • @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 +2

      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.

  • @danielcervini2545
    @danielcervini2545 2 года назад

    Are you an angel?

  • @sohamsantra7548
    @sohamsantra7548 3 года назад

    This channel should be renamed to Grade saving tutor!

  • @xk3113
    @xk3113 4 года назад +1

    This topic is hard

  • @yasmeenkarachiwala9612
    @yasmeenkarachiwala9612 4 года назад

    Why is n constant?

    • @tansy2279
      @tansy2279 4 года назад +1

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

  • @blackholesun4942
    @blackholesun4942 9 месяцев назад

    Thanks you

  • @AnjuSingh-vm8wy
    @AnjuSingh-vm8wy Год назад

    God bless you

  • @serinacat4781
    @serinacat4781 4 года назад +1

    These saves my ass

  • @Sunita_Notiyal
    @Sunita_Notiyal Год назад

    Mississippi

  • @abinjohn8133
    @abinjohn8133 4 года назад

    Dark blue is a little too dark

    • @tansy2279
      @tansy2279 4 года назад

      Seems pretty bright to me

  • @divineaxel9764
    @divineaxel9764 4 года назад

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

  • @goksuphysics
    @goksuphysics 7 месяцев назад

    bro i will get a 100 for you

  • @omegabowl6857
    @omegabowl6857 5 лет назад

    i fucking love you

  • @amruthadhanabalan1328
    @amruthadhanabalan1328 6 лет назад +2

    Cooooooooooooolllllll

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

    💛💛💛💛💛💛💛💛

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

    💛💛💛💛

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

    💛💛💛

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

    شريف

  • @lucyferguson9020
    @lucyferguson9020 3 года назад

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

  • @violethill4454
    @violethill4454 Год назад

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