What is Integration? Finding the Area Under a Curve

Ok, we've wrapped up differential calculus, so it's time to tackle integral calculus! It's definitely the trickier of the two, but don't worry, it's nothing you can't handle! First things first, what is integration? Well it's that thing we mentioned way back in the introduction clip, when we talked about adding up the infinite tiny rectangles. Just watch and you'll see!
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Пікірлер: 196

  • @tbax4259
    @tbax42595 жыл бұрын

    Dear Professor Dave, you explained integration to me in just under nine minutes. WOW. Thanks, Professor Dave. I am now your happiest patron!

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    5 жыл бұрын

    thanks for your support!

  • @thefact6225

    @thefact6225

    2 жыл бұрын

    @@ProfessorDaveExplains please explain about you

  • @marekjanik9962
    @marekjanik99625 жыл бұрын

    Thank You professor Jesus

  • @BrandedDevil

    @BrandedDevil

    5 жыл бұрын

    Lol 😂😂

  • @junesept234

    @junesept234

    5 жыл бұрын

    lol.

  • @linccodes

    @linccodes

    3 жыл бұрын

    Yeah.... Coz he's the school messiah for last minute study.... Lol 😅

  • @naomiaemanuel7187

    @naomiaemanuel7187

    3 жыл бұрын

    Matnematics is the status of the world to have his own life experience as a good place to students and to be the best way to do this in the future of your business and how you can get the most important information to make your business is not the only ones that can who you want to do for the I know that you are so cDvlD and you are not the only ones that can who you want to do for the cDvlD of your life in the world of music and the world to have his own life experience

  • @Mindochin03

    @Mindochin03

    3 жыл бұрын

    Amen to that

  • @therealdeal6659
    @therealdeal66595 жыл бұрын

    Nice, this is way better than binge watching Netflix.

  • @junesept234

    @junesept234

    5 жыл бұрын

    Then, after watching this, try to watch 3Brown1Brown. It is nice to complement this video to the videos of 3Blue1Brown.

  • @therealdeal6659

    @therealdeal6659

    5 жыл бұрын

    Rinkazhi Rinkashime Lol of course, his videos give a much deeper conceptual understanding of the subject matter. However, the procedure itself is covered more in Professor Dave’s videos.

  • @pinklady7184

    @pinklady7184

    4 жыл бұрын

    You have said it. I watch video tutorials more than watching TV.

  • @9308323

    @9308323

    4 жыл бұрын

    @@pinklady7184 You still watch TV!?

  • @pinklady7184

    @pinklady7184

    4 жыл бұрын

    930 8323 Very rarely. I haven't watched TV in many months. After work, I usually go straight to bed and watch tutorials on tablet or read ebooks at Open Library. Just yesterday, my sister bought a large TV screen and installed it in our home. The new TV is ENORMOUS and screen resolutions is high. It comes with wifi. Last night, I was watching Blender tutorials (3D modelling) on KZread, all on TV screen. The thumbnails of drama and documentaries on TV look VERY ENTICING and TEMPTING. I resisted temptations.

  • @74Gee
    @74Gee2 жыл бұрын

    As a programmer who didn't learn calculus, integrations or anything else like that, this is GOLD. Thank you!

  • @sarahfox3652
    @sarahfox36523 жыл бұрын

    You are literally my Calc II teacher right now thanks to distance learning lol so THANK YOU!! This was very helpful!! We need content like this now more than ever.

  • @drewpetersen3683
    @drewpetersen36834 жыл бұрын

    Your videos are explained so well! Thank you! The time put into these animations really reflects the viewers ability to understand it as well! Keep it up! Also this unit is actually pretty interesting. I never thought I would hear myself say math is interesting but seeing how calculus finally folds out is kinda cool.

  • @joeykenn
    @joeykenn3 жыл бұрын

    An excellent simple well illustrated explanation. Thank you very much.

  • @varunn.a.5764
    @varunn.a.576411 ай бұрын

    My teacher never taught me all that when I was at school...When I watched a video related to entropy , I got scared by the integral sign just like the way I got when I was back in high school. I work as an automation engineer in food and pharma sector and have watched some of your nice videos related to pharma industry. Now I have got the clearer idea of why integration is important and hoping to make use of the knowledge in future. Now I also realize how bad the situation was for us before these videos become available. Professor Dave inspires me to face my old high school and college demons and win the fights I lost back then. Teachers like you provide us with an opportunity to fix the gaps we had in our early education and provide us confidence to upgrade our brains for the future....Great Video and wishing the best for you and your channel😃

  • @Maryam-dq1iy
    @Maryam-dq1iy Жыл бұрын

    Thank you very much for your effort in explaining these hard topics, really appreciated

  • @isaiahrichards9319
    @isaiahrichards93193 жыл бұрын

    Wow, this really helped me to understand. Thank you very much!

  • @siddhantshenvi5006
    @siddhantshenvi50062 жыл бұрын

    Superb explanation...it's crystal clear...Thank you so much Professor Dave!!

  • @apostolosfilippos
    @apostolosfilippos2 жыл бұрын

    I hated this for over 20 years. Explained in 8 minutes. Thank you!

  • @3deeguy
    @3deeguy6 жыл бұрын

    Thank you for explaining how to identify the part of the equation that identifies the height of the rectangle and the part that identifies the base. I will not move on to fourier transforms until calculus makes sense to me. I think I need to work on a few examples to let it sink in.

  • @niv5883
    @niv58834 жыл бұрын

    Ad: still search for math help are the videos from 2006 really helping? Me :yes

  • @physicsforever4793
    @physicsforever47933 жыл бұрын

    This was a great explanation!

  • @Squash101
    @Squash1012 жыл бұрын

    This is absolutely incredible.

  • @LvHTube
    @LvHTube5 жыл бұрын

    You explain very clear, thxs

  • @Thaumius
    @Thaumius6 жыл бұрын

    Hey Dave, my teacher taught us about left hand rule, right hand rule and midpoint rule, how do you implement them into the summation formula (Riemann sum)?

  • @odileabimana
    @odileabimana3 жыл бұрын

    you saved me. Thank you so much for this tutorial

  • @gamingwithtrikku2371
    @gamingwithtrikku23712 жыл бұрын

    Thank you professor Dave!

  • @ripperduck
    @ripperduck5 жыл бұрын

    I very much appreciate the work you've put into your series of vids. But, the problem is that no one explains why calculus was invented, why it works with physics, what the area of an integral is suppose to physically mean, on and on. As a guy with a BS Physics, not one professor, nor textbook, ever bothered to explain/lecture the 'why' of math, which meant, that for many years, we were doing things by simple memorization. What I learned is that the most important math concept is that of the pure number. Derivatives and integrals are pure numbers, as are fractions, ratios, percentages, geometry, trig, slopes, thermo entropy, and a bunch of other things. In other words, we were introduced to the overarching concept of all calculus back in the third grade, but no one bothered to explain its importance. I wish STEM vids would begin teaching the fundamental concepts of their disciplines prior to doing problems, that way the subject matter would be far more engaging...

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    5 жыл бұрын

    Check out my tutorial introducing calculus. It’s the first in my calculus playlist. I teach precisely what you’re asking for.

  • @erazn9077

    @erazn9077

    2 жыл бұрын

    Absolutely! That’s honestly the worst part about math, that nobody explains why we’re doing what we’re doing. When you get past that though math get pretty fun lol

  • @minorfirestar2433
    @minorfirestar24333 жыл бұрын

    Thank you so much for the Calculus videos, Professor Dave! I'm about to take a CLEP exam for Calc. and the study videos I originally used (by Modern States) were no help at all. More people need to know about you!

  • @hikmatullahpakhtoon3694
    @hikmatullahpakhtoon36944 жыл бұрын

    wow interesting and an incredible way of teaching, i like it

  • @user-sm9up1zk6w
    @user-sm9up1zk6w3 ай бұрын

    Thank you so much. That was really useful

  • @vijayshirsath3170
    @vijayshirsath31703 жыл бұрын

    Great explanations

  • @deepaktiwari7059
    @deepaktiwari70594 жыл бұрын

    Thank you so much!

  • @SchwanaCARDHUT
    @SchwanaCARDHUT5 жыл бұрын

    thanks for this explication .

  • @karanmali6847
    @karanmali68475 жыл бұрын

    Thank you so much sir

  • @swarrnarathna6633
    @swarrnarathna66334 жыл бұрын

    its really helpfull sir .thank you

  • @blazetech6614
    @blazetech6614 Жыл бұрын

    Thank you Prof

  • @dimqueen7624
    @dimqueen76246 жыл бұрын

    You are perfect

  • @junaidbangash3969
    @junaidbangash39694 жыл бұрын

    Thanks great lecture

  • @udayveersingh2738
    @udayveersingh27383 жыл бұрын

    Nice understanding

  • @vivianperalta7378
    @vivianperalta73785 жыл бұрын

    Amazingggggggggggggggggggg. more people should watch your channel

  • @wisdom_wellness365
    @wisdom_wellness3653 жыл бұрын

    Very nice! I like it!

  • @TheShash18
    @TheShash183 жыл бұрын

    This is just amazing..!

  • @saritaprasad4295
    @saritaprasad42957 ай бұрын

    Nice explanation

  • @0916079787
    @09160797873 жыл бұрын

    Wow that's great, thank you.

  • @karthick5493
    @karthick54934 жыл бұрын

    Thank you professor

  • @nithinsirimanne2924
    @nithinsirimanne29249 ай бұрын

    Thanks this is so easy

  • @lordoftheunholyponys
    @lordoftheunholyponys4 жыл бұрын

    i love you, dave.

  • @MrHigoli
    @MrHigoli5 жыл бұрын

    thx a lot prof. your awesome

  • @dont4629
    @dont46292 жыл бұрын

    Thank you so much 🙏❤️💯💯

  • @MathsWithMichalis
    @MathsWithMichalis3 жыл бұрын

    Amazing explanation by Dave I am a math tutor... this video is perfect

  • @juliansthoughts5641
    @juliansthoughts56413 жыл бұрын

    Omg. Thank you. Purely

  • @leonisaacs3512
    @leonisaacs35124 жыл бұрын

    Thanks!

  • @adityashankar5267
    @adityashankar52675 жыл бұрын

    Hello...Do we need to manually calculate the areas of all kinda rectangles and find out what value they approach? I mean, isn't there any formula..

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    5 жыл бұрын

    keep watching through the series and find out!

  • @alexanderchronos8694
    @alexanderchronos86946 жыл бұрын

    I'd wait a week for the next video.

  • @chloecraig3202
    @chloecraig32022 жыл бұрын

    We love you professor Dave

  • @_____758
    @_____7583 жыл бұрын

    thank goodness! someone finally makes sense lol

  • @shamassadaf9040
    @shamassadaf90406 жыл бұрын

    Gr8 video professor, thanx

  • @livetodraw5939
    @livetodraw5939 Жыл бұрын

    I in the 5th grade and you help me understand so well 😊 thank you

  • @satbirsingh7269
    @satbirsingh72696 жыл бұрын

    Sir i have problem to prove a function onto and one one plz tell me something for which i can do best!!!

  • @TopG20073
    @TopG20073 Жыл бұрын

    Thanks

  • @qaphelaminenhle3173
    @qaphelaminenhle31733 жыл бұрын

    thank you

  • @TheRiptideXD
    @TheRiptideXD3 жыл бұрын

    Damn crit1kals really branching out these days

  • @CyberS_1984
    @CyberS_1984 Жыл бұрын

    Does a horizontal asymtote between the curve and the x-axis require any alteration to the process? Thanks

  • @scoopboy
    @scoopboy Жыл бұрын

    Proffessor Dave you game an epiphany at 3:33

  • @r.ganeshm7336
    @r.ganeshm73364 жыл бұрын

    Hi Mr.Dave , pls reply for my doubt. For circle , parabola, sphere's we have general equation. Why polygons doesn't have any equation?

  • @carultch

    @carultch

    2 жыл бұрын

    Polygons are not infinitely differentiable like circles, parabolas, and spheres. You need a piecewise function to define a polygon, because you have jump discontinuities in their slopes at every corner.

  • @r.ganeshm7336

    @r.ganeshm7336

    2 жыл бұрын

    @@carultch thank you so much.

  • @ian.ambrose
    @ian.ambrose2 жыл бұрын

    This video is GOOOOOOOOOOOOOD

  • @bekalutadesse8615
    @bekalutadesse86153 жыл бұрын

    Always make conceptualize more

  • @Crbecker2
    @Crbecker22 жыл бұрын

    TENGO EXAMENAAA

  • @erikaespina
    @erikaespina Жыл бұрын

    thank you🥲

  • @riyagalhotra4393
    @riyagalhotra43933 жыл бұрын

    Very nyc video🙇‍♂️🙇‍♂️

  • @johnpro2847
    @johnpro28474 жыл бұрын

    1:18 The class room gives you a function .how do you get the area when a function is not know as in the shape presented ?

  • @Ahmed-vs1ui

    @Ahmed-vs1ui

    3 жыл бұрын

    Ofc u cant there are no dimensions given its like drawing a square and asking u for its area without giving u a side length u must know the function

  • @nazuu
    @nazuu3 жыл бұрын

    Thanks =)

  • @jrlizardking
    @jrlizardking5 жыл бұрын

    Hey anyway I could pay you for tutoring on Skype or something. Thanks

  • @AlexusDelphi
    @AlexusDelphi Жыл бұрын

    You explained better in the first 5 minutes than my professor did in 30

  • @frank4282
    @frank428211 ай бұрын

    What if I see a graph but I can't discover a function out of it to integrate? I have a graph from solar power generation in a day but can't find its function. Each points give a different y(Except vertex).

  • @Bel...QWERTY1
    @Bel...QWERTY16 ай бұрын

    Please .. tell us how to get the intergration rules like : Intergration of x^2 is x^3/3 + C Why is that how they get it for the first time ???

  • @schifoso
    @schifoso6 жыл бұрын

    It's amazing that Archimedes was using inscribed polygons to approximate areas of curved surfaces. If he would have taken the number of inscriptions to infinity, he might have invented calculus a couple thousand years before Newton.

  • @ubaidshah1910

    @ubaidshah1910

    5 жыл бұрын

    Archimedes is a fake character who never existed

  • @BG-wm2tw

    @BG-wm2tw

    4 жыл бұрын

    Ubaid Shah ..... F off idiot. F**ing clueless moron.

  • @BG-wm2tw

    @BG-wm2tw

    4 жыл бұрын

    Robert Zanatta .. I agree.

  • @idontknow1630

    @idontknow1630

    Жыл бұрын

    @Leonhard Euler what does religion have to do with this?

  • @johnkhan7966
    @johnkhan79664 жыл бұрын

    mountain has a curve shape then how we split a mountain in to a bunch of rectangles, please reply if some one has the answer

  • @charlie3k

    @charlie3k

    4 жыл бұрын

    split it into an infinite amount of rectangles

  • @johnkhan7966

    @johnkhan7966

    4 жыл бұрын

    how you splits mountain

  • @tia4361

    @tia4361

    4 жыл бұрын

    You don't split a mountain, it's purely hypothetical. It's an example of approximating the area.

  • @Julia27201
    @Julia272013 жыл бұрын

    Question- why not divide it into one triangle? (3:48)

  • @anilkumarsharma1205
    @anilkumarsharma12054 жыл бұрын

    how volume of spheroid and oloyed are correlated with their volume

  • @kelsiebattle5993
    @kelsiebattle59933 жыл бұрын

    Can you explain how to apply that equation pleaseee???

  • @papermario2169
    @papermario21696 жыл бұрын

    Professor Dave, if you are a patreon are u able to schedule one on one coaching for a set period of time? It would be dank if Patreons got one on one Skype time for a certain amount of time that is paid of course.

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    6 жыл бұрын

    Well I do have an option as one of the tiers on Patreon where you get an hour of Skype tutoring per month! However, it is my highest tier. But it's there for you!

  • @fashionwithme3198
    @fashionwithme31983 ай бұрын

    The intro was also good😂

  • @basselsy3337
    @basselsy33374 жыл бұрын

    What the best books to learn Mathematics?

  • @sweatypineapple4411
    @sweatypineapple441126 күн бұрын

    I love you dave

  • @imsavage2449
    @imsavage24494 жыл бұрын

    whos here just to see the intro

  • @tushargupta6304
    @tushargupta6304 Жыл бұрын

    Wht about connection between differentiation and integration

  • @choo1030
    @choo10303 жыл бұрын

    I have 2 Calculus professor. One is getting paid with my tuition, the other received zero cent from me for quality lecture videos. Yet, the one getting unpaid clearly can teach WAY BETTER than the paid one. My money is clearly getting wasted!!!!

  • @TopG20073
    @TopG20073 Жыл бұрын

    Can’t we subtract the area of the triangles by the area of the rectangles?

  • @eziosdiy1504
    @eziosdiy15044 жыл бұрын

    Subscribed

  • @md.jahangeralam3988
    @md.jahangeralam39883 ай бұрын

    Just wow...

  • @APXSTUDIO
    @APXSTUDIO8 ай бұрын

    OHHHHHHHH I ALWAYS WONDERED WHY INTEGRATION IS USED OR WHY IS IT SO HYPED SO THE MAIN USE FOR INTEGRATION IS FINDING AN AREA UNDER CURVE THANK YOU SOOO MUCH I DONT REALLY PAY ATTENTION IN CLASS SINCE I ALWAYS DAY DREAM

  • @tGoldenPhoenix
    @tGoldenPhoenix2 жыл бұрын

    Done.

  • @ianloveservice
    @ianloveservice3 жыл бұрын

    You save my life

  • @superpussycat6648
    @superpussycat66484 жыл бұрын

    Thanks Prof Jesus.

  • @gheorghechilnicean5530
    @gheorghechilnicean55303 жыл бұрын

    For better understanding give us an exemple wich has a concret ancer in m^2

  • @carultch

    @carultch

    Жыл бұрын

    Ok: a slab of concrete starts at the origin, and is 10 meters wide along the x-axis. The remaining perimeter to this width, is defined by the function y=-x*(x-10)/5, where x and y have units of meters. Calculate the area covered by this slab of concrete.

  • @AbdulRehmanAbdulAziz
    @AbdulRehmanAbdulAziz5 жыл бұрын

    How to calculate incremental area under curve

  • @totalfreedom45
    @totalfreedom452 жыл бұрын

    Professor Dave rocks and rolls; although he looks like a rock star, he is not a rock star but a cool math teacher. 😂 💕 ☮ 🌎 🌌

  • @anilkumarsharma1205
    @anilkumarsharma12054 жыл бұрын

    relationship between function and its derivative and it's integral are how correlated with each other so we know that how much percentage are more or less they are, correlation coefficient and percentage related with real function like volume of the spherical shape and it's surface area are derivation for round circle and sphere now we want to know about cubic or cuboid systems that how their volume and surface area are correlated

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    4 жыл бұрын

    go through my calculus playlist, it will help!

  • @angryhulk7099
    @angryhulk70995 жыл бұрын

    Is there anyway to find area under curve without using approximation sir.....

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    5 жыл бұрын

    check out the very next tutorial on the fundamental theorem of calculus and you'll see!

  • @matokurin
    @matokurin3 жыл бұрын

    Thank you. Professor Jesus

  • @ian.ambrose

    @ian.ambrose

    2 жыл бұрын

    lmao

  • @adityaverma6980
    @adityaverma69804 жыл бұрын

    when there will be thousand of small rectangles how we well add them all? i have watch hundered of videos of you tube but no teacher can give the answer of this question

  • @DeepakSharma-pt4gh

    @DeepakSharma-pt4gh

    3 жыл бұрын

    We will suppose to all like n.

  • @tea1594
    @tea15943 жыл бұрын

    I LOVE YOU

  • @kushagrasingh9624
    @kushagrasingh96243 жыл бұрын

    How performing integration adds area of those tiny rectangles means integration just change slope into function

  • @treycoble4331
    @treycoble43312 жыл бұрын

    I’m not even in calc but I still think this is cool lol

  • @ramk1985
    @ramk19855 жыл бұрын

    but how is it possible to find the areas of infinte rectangles and add those up

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    5 жыл бұрын

    Maybe start at the beginning of the calculus series with the introduction, it explains precisely how you can do something infinite times and get a finite answer, which is what calculus is all about!