What is Integration? Finding the Area Under a Curve

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  • เผยแพร่เมื่อ 25 ส.ค. 2024

ความคิดเห็น • 205

  • @tbax4259
    @tbax4259 5 ปีที่แล้ว +217

    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 ปีที่แล้ว +53

      thanks for your support!

    • @thefact6225
      @thefact6225 3 ปีที่แล้ว +1

      @@ProfessorDaveExplains please explain about you

  • @marekjanik9962
    @marekjanik9962 5 ปีที่แล้ว +752

    Thank You professor Jesus

    • @BrandedDevil
      @BrandedDevil 5 ปีที่แล้ว +13

      Lol 😂😂

    • @junesept234
      @junesept234 5 ปีที่แล้ว +7

      lol.

    • @linccodes
      @linccodes 4 ปีที่แล้ว +15

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

    • @naomiaemanuel7187
      @naomiaemanuel7187 3 ปีที่แล้ว

      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 ปีที่แล้ว +2

      Amen to that

  • @74Gee
    @74Gee 2 ปีที่แล้ว +33

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

  • @therealdeal6659
    @therealdeal6659 5 ปีที่แล้ว +182

    Nice, this is way better than binge watching Netflix.

    • @junesept234
      @junesept234 5 ปีที่แล้ว +10

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

    • @therealdeal6659
      @therealdeal6659 5 ปีที่แล้ว +2

      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 ปีที่แล้ว +5

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

    • @9308323
      @9308323 4 ปีที่แล้ว +1

      @@pinklady7184 You still watch TV!?

    • @pinklady7184
      @pinklady7184 4 ปีที่แล้ว +5

      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 TH-cam, all on TV screen.
      The thumbnails of drama and documentaries on TV look VERY ENTICING and TEMPTING. I resisted temptations.

  • @varunn.a.5764
    @varunn.a.5764 ปีที่แล้ว +5

    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😃

  • @sarahfox3652
    @sarahfox3652 3 ปีที่แล้ว +11

    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.

  • @niv5883
    @niv5883 4 ปีที่แล้ว +14

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

  • @drewpetersen3683
    @drewpetersen3683 4 ปีที่แล้ว +33

    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.

  • @ripperduck
    @ripperduck 5 ปีที่แล้ว +11

    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 ปีที่แล้ว +5

      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 ปีที่แล้ว +2

      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

  • @apostolosfilippos
    @apostolosfilippos 2 ปีที่แล้ว +7

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

  • @joeykenn
    @joeykenn 3 ปีที่แล้ว +5

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

  • @isaiahrichards9319
    @isaiahrichards9319 3 ปีที่แล้ว +9

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

  • @Kiky_MedPhysicist
    @Kiky_MedPhysicist 2 วันที่ผ่านมา

    Thank you sir for your dedication and for making this free! 🙏

  • @waeastconstituency5400
    @waeastconstituency5400 หลายเดือนก่อน

    Needed this 15 years ago. Thank you

  • @3deeguy
    @3deeguy 6 ปีที่แล้ว +5

    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.

  • @Maryam-dq1iy
    @Maryam-dq1iy ปีที่แล้ว +2

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

  • @odileabimana
    @odileabimana 3 ปีที่แล้ว +3

    you saved me. Thank you so much for this tutorial

  • @dimqueen7624
    @dimqueen7624 6 ปีที่แล้ว +21

    You are perfect

  • @AA-eq5wk
    @AA-eq5wk 16 วันที่ผ่านมา

    the quantum wave function is a positive AND negative swing which "differentiates" the parts or two poles that make up a whole; the "integration" is then taking that entirety and making a "relativity" or relative observation which is not true to the whole but polarized... in order for a 3 dimensional life form to interact with a solid or 3-D world, the observation must polarize the wave function so that it can be compared to other measurements or become a finite piece in an infinite whole...

  • @Thaumius
    @Thaumius 6 ปีที่แล้ว +10

    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)?

  • @_____758
    @_____758 4 ปีที่แล้ว +8

    thank goodness! someone finally makes sense lol

  • @scoopboy
    @scoopboy ปีที่แล้ว +2

    Proffessor Dave you game an epiphany at 3:33

  • @physicsforever4793
    @physicsforever4793 4 ปีที่แล้ว +3

    This was a great explanation!

  • @siddhantshenvi5006
    @siddhantshenvi5006 2 ปีที่แล้ว +1

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

  • @Squash101
    @Squash101 2 ปีที่แล้ว +1

    This is absolutely incredible.

  • @adityashankar5267
    @adityashankar5267 5 ปีที่แล้ว +5

    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..

  • @schifoso
    @schifoso 6 ปีที่แล้ว +4

    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 ปีที่แล้ว

      Archimedes is a fake character who never existed

    • @user-wm2tw
      @user-wm2tw 4 ปีที่แล้ว

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

    • @user-wm2tw
      @user-wm2tw 4 ปีที่แล้ว

      Robert Zanatta .. I agree.

    • @idontknow1630
      @idontknow1630 ปีที่แล้ว

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

  • @TheRiptideXD
    @TheRiptideXD 3 ปีที่แล้ว +6

    Damn crit1kals really branching out these days

  • @user-rk4bo8uw4y
    @user-rk4bo8uw4y หลายเดือนก่อน

    You earned my subscription always

  • @JAyjofirst
    @JAyjofirst หลายเดือนก่อน

    Thank you very much for this Video 🙏🏼

  • @bekalutadesse8615
    @bekalutadesse8615 3 ปีที่แล้ว +1

    Always make conceptualize more

  • @hikmatullahpakhtoon3694
    @hikmatullahpakhtoon3694 4 ปีที่แล้ว +2

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

  • @blazetech6614
    @blazetech6614 2 ปีที่แล้ว +1

    Thank you Prof

  • @lordoftheunholyponys
    @lordoftheunholyponys 4 ปีที่แล้ว +2

    i love you, dave.

  • @vivianperalta7378
    @vivianperalta7378 5 ปีที่แล้ว +1

    Amazingggggggggggggggggggg. more people should watch your channel

  • @APXSTUDIO
    @APXSTUDIO 10 หลายเดือนก่อน

    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

  • @LvHTube
    @LvHTube 5 ปีที่แล้ว +1

    You explain very clear, thxs

  • @shamassadaf9040
    @shamassadaf9040 6 ปีที่แล้ว +5

    Gr8 video professor, thanx

  • @choo1030
    @choo1030 3 ปีที่แล้ว +1

    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!!!!

  • @livetodraw5939
    @livetodraw5939 ปีที่แล้ว

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

  • @user-sm9up1zk6w
    @user-sm9up1zk6w 6 หลายเดือนก่อน

    Thank you so much. That was really useful

  • @minorfirestar
    @minorfirestar 3 ปีที่แล้ว

    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!

  • @johnkhan7966
    @johnkhan7966 5 ปีที่แล้ว +4

    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 5 ปีที่แล้ว

      split it into an infinite amount of rectangles

    • @johnkhan7966
      @johnkhan7966 4 ปีที่แล้ว

      how you splits mountain

    • @tia4361
      @tia4361 4 ปีที่แล้ว +5

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

  • @alexanderchronos8694
    @alexanderchronos8694 6 ปีที่แล้ว +2

    I'd wait a week for the next video.

  • @fashionwithme3198
    @fashionwithme3198 6 หลายเดือนก่อน

    The intro was also good😂

  • @udayveersingh2738
    @udayveersingh2738 3 ปีที่แล้ว

    Nice understanding

  • @TopG20073
    @TopG20073 ปีที่แล้ว

    Thanks

  • @r.ganeshm7336
    @r.ganeshm7336 4 ปีที่แล้ว +3

    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 ปีที่แล้ว

      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 ปีที่แล้ว

      @@carultch thank you so much.

  • @saritaprasad4295
    @saritaprasad4295 10 หลายเดือนก่อน

    Nice explanation

  • @MathsWithMichalis
    @MathsWithMichalis 3 ปีที่แล้ว

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

  • @tushargupta6304
    @tushargupta6304 ปีที่แล้ว

    Wht about connection between differentiation and integration

  • @gamingwithtrikku2371
    @gamingwithtrikku2371 3 ปีที่แล้ว

    Thank you professor Dave!

  • @vijayshirsath3170
    @vijayshirsath3170 3 ปีที่แล้ว

    Great explanations

  • @AlexusDelphi
    @AlexusDelphi ปีที่แล้ว

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

  • @chloecraig3202
    @chloecraig3202 2 ปีที่แล้ว

    We love you professor Dave

  • @erikaespina
    @erikaespina ปีที่แล้ว

    thank you🥲

  • @nithinsirimanne2924
    @nithinsirimanne2924 ปีที่แล้ว

    Thanks this is so easy

  • @junaidbangash3969
    @junaidbangash3969 4 ปีที่แล้ว

    Thanks great lecture

  • @user-gu3hv6jd9c
    @user-gu3hv6jd9c 4 ปีที่แล้ว

    Wow that's great, thank you.

  • @deepaktiwari7059
    @deepaktiwari7059 4 ปีที่แล้ว

    Thank you so much!

  • @wisdom_wellness365
    @wisdom_wellness365 3 ปีที่แล้ว

    Very nice! I like it!

  • @Crbecker2
    @Crbecker2 2 ปีที่แล้ว +3

    TENGO EXAMENAAA

  • @karthick5493
    @karthick5493 4 ปีที่แล้ว

    Thank you professor

  • @swarrnarathna6633
    @swarrnarathna6633 5 ปีที่แล้ว

    its really helpfull
    sir .thank you

  • @dont4629
    @dont4629 2 ปีที่แล้ว

    Thank you so much 🙏❤️💯💯

  • @juliansthoughts5641
    @juliansthoughts5641 3 ปีที่แล้ว

    Omg. Thank you. Purely

  • @jrlizardking
    @jrlizardking 5 ปีที่แล้ว +7

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

  • @aselim20.
    @aselim20. ปีที่แล้ว +2

    I wrote it.

  • @karanmali6847
    @karanmali6847 5 ปีที่แล้ว

    Thank you so much sir

  • @imsavage2449
    @imsavage2449 5 ปีที่แล้ว +11

    whos here just to see the intro

  • @gheorghechilnicean5530
    @gheorghechilnicean5530 3 ปีที่แล้ว

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

    • @carultch
      @carultch ปีที่แล้ว

      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.

  • @TheShash18
    @TheShash18 3 ปีที่แล้ว

    This is just amazing..!

  • @qaphelaminenhle3173
    @qaphelaminenhle3173 3 ปีที่แล้ว

    thank you

  • @SchwanaCARDHUT
    @SchwanaCARDHUT 5 ปีที่แล้ว

    thanks for this explication .

  • @totalfreedom45
    @totalfreedom45 2 ปีที่แล้ว +1

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

  • @leonisaacs3512
    @leonisaacs3512 4 ปีที่แล้ว

    Thanks!

  • @Bel...QWERTY1
    @Bel...QWERTY1 9 หลายเดือนก่อน

    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 ???

  • @TopG20073
    @TopG20073 ปีที่แล้ว

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

  • @MrHigoli
    @MrHigoli 5 ปีที่แล้ว

    thx a lot prof. your awesome

  • @kelsiebattle5993
    @kelsiebattle5993 3 ปีที่แล้ว

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

  • @Julia27201
    @Julia27201 3 ปีที่แล้ว

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

  • @tGoldenPhoenix
    @tGoldenPhoenix 2 ปีที่แล้ว

    Done.

  • @riyagalhotra4393
    @riyagalhotra4393 3 ปีที่แล้ว

    Very nyc video🙇‍♂️🙇‍♂️

  • @CyberS_1984
    @CyberS_1984 ปีที่แล้ว

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

  • @angryhulk7099
    @angryhulk7099 5 ปีที่แล้ว +1

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

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  5 ปีที่แล้ว

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

  • @frank4282
    @frank4282 ปีที่แล้ว

    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).

  • @nazuu
    @nazuu 4 ปีที่แล้ว

    Thanks =)

  • @ian.ambrose
    @ian.ambrose 2 ปีที่แล้ว

    This video is GOOOOOOOOOOOOOD

  • @kushagrasingh9624
    @kushagrasingh9624 3 ปีที่แล้ว +1

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

  • @sweatypineapple4411
    @sweatypineapple4411 3 หลายเดือนก่อน

    I love you dave

  • @eziosdiy1504
    @eziosdiy1504 4 ปีที่แล้ว

    Subscribed

  • @matokurin
    @matokurin 3 ปีที่แล้ว

    Thank you. Professor Jesus

  • @md.jahangeralam3988
    @md.jahangeralam3988 5 หลายเดือนก่อน

    Just wow...

  • @satbirsingh7269
    @satbirsingh7269 6 ปีที่แล้ว

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

  • @ianloveservice
    @ianloveservice 3 ปีที่แล้ว

    You save my life

  • @basselsy3337
    @basselsy3337 4 ปีที่แล้ว

    What the best books to learn Mathematics?

  • @johnpro2847
    @johnpro2847 4 ปีที่แล้ว

    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 ปีที่แล้ว +1

      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

  • @superpussycat6648
    @superpussycat6648 4 ปีที่แล้ว

    Thanks Prof Jesus.

  • @anilkumarsharma1205
    @anilkumarsharma1205 4 ปีที่แล้ว

    how volume of spheroid and oloyed are correlated with their volume

  • @anilkumarsharma1205
    @anilkumarsharma1205 4 ปีที่แล้ว

    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