Double and Triple Integrals

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  • Опубліковано 20 сер 2019
  • Remember the good old calculus days, and all that time we spent with integration? Let's go back! Oh calm down, it wasn't that bad. Besides, we won't be learning anything terribly new, we will just look at double integrals and triple integrals, which are pretty much the same as single integrals, we just integrate more than once. But admittedly it can be a little tricky to set up the bounds of integration and choose the order in which we integrate each variable, so let's go through the rules and some examples.
    Script by Howard Whittle
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КОМЕНТАРІ • 361

  • @schifoso
    @schifoso 4 роки тому +565

    You are such a great teacher.
    And I like how you use "we" instead of "you". Makes the student feel like they are not alone.

    • @MegaYoungscientist
      @MegaYoungscientist 3 роки тому +25

      I think it's great because even the professors still are students at the end of the day, because everyone is still learning more about their subjects.

  • @GiangTranAI
    @GiangTranAI 4 роки тому +676

    Best teachers so far: 3blue1brown and Professor Dave.

    • @hzkzg1614
      @hzkzg1614 4 роки тому +53

      You seriously wouldnt count sal or Patrickjmt?

    • @adityarajsrivastava6580
      @adityarajsrivastava6580 4 роки тому +101

      Blackpenredpen

    • @garethpienaar3119
      @garethpienaar3119 3 роки тому +42

      Professor Leonard is the best for me, by far

    • @gouravgope1367
      @gouravgope1367 3 роки тому +15

      Zach star

    • @jorge_cazares
      @jorge_cazares 3 роки тому +8

      For me, the best teachers so far are: Professor Gross, from MIT OCW Calculus Revisited, 3blue1brown, and Professor Dave

  • @buttersquids
    @buttersquids Рік тому +19

    I was struggling a lot on understanding double integrals on a homework assignment, but this helped massively. Thanks Dave!

  • @theresaread6174
    @theresaread6174 3 роки тому +50

    Blessings upon you, Dave. Two minutes in and you’ve already made this make more sense than my instructor.

  • @akuo0708
    @akuo0708 Місяць тому +6

    this is the clearest explaining math video i've ever watched

  • @mikepablo
    @mikepablo 4 роки тому +10

    Brilliant , wish I had this when I did maths so much clearer and simple, during lock down going though my old notes 30 years ago inspired me to study more

  • @lemonhscott7667
    @lemonhscott7667 4 місяці тому

    Professor Dave, thank you so much for these resources! They've been a huge help to me in ODELA and Vector Calc. I'd be lost without you!

  • @mastershooter64
    @mastershooter64 4 роки тому +130

    So you can actually find the volume inside a tesseract niceees

    • @kek3324
      @kek3324 4 роки тому +20

      its a hypervolume

    • @JorgetePanete
      @JorgetePanete 4 роки тому +14

      @@kek3324 It's*

    • @doxo9597
      @doxo9597 4 роки тому +36

      Jorge C. M. I can tell you have a lot of friends.

    • @OneDerscoreOneder
      @OneDerscoreOneder 4 роки тому +7

      It’s just all the side lengths multiplied

    • @dinamosflams
      @dinamosflams 4 роки тому +4

      You can find both, the volume and the hypervolume of a tesseract. Although I think it's more difficult to grasp the concept of the volume of a tesseract

  • @ActionJaxonH
    @ActionJaxonH 4 роки тому +32

    This video is amazing. I’m self taught, going through Professor Leonard’s Calc 3 YT series course, and double and triple integrals are coming up in the very near future so I wanted to get a head start. This is totally logical and it just makes sense

    • @extremeforlife8563
      @extremeforlife8563 Рік тому +1

      Thanks, I checked out the series after seeing your comment. It is more suited to what I am looking for. Really appreciate it man.

  • @FlyByPC
    @FlyByPC 4 роки тому +35

    Great explanation!
    Of course, my inclination is still to hit it with a FOR loop...

  • @harishkumar-rn2mw
    @harishkumar-rn2mw 3 роки тому +28

    Hi Dave, I got confused in the part choosing lower bound and upper bound between 2 cuves. Pls explain..

  • @lukafarkas420
    @lukafarkas420 Рік тому

    good job Dave, you have explained this to me in a most understandable way possible, with clear color indications, thank you sir.

  • @georgefan2977
    @georgefan2977 4 роки тому +8

    Thank you, that was one of the most straightfoward explaination!

  • @cd8836
    @cd8836 9 місяців тому +1

    Thank you for the videos. They help a lot! I’ve had a mental block about these topics for decades.

  • @shaiyongcheng9721
    @shaiyongcheng9721 3 роки тому +7

    This video is better than 1 hour of lecture. Tq very much

  • @johnsnow3444
    @johnsnow3444 2 місяці тому

    Was so thrilled when i did the double integral the other way from y/2 to (y)^1/2 and got the same answer! strangely that way took up less paper. Thanks for the solid content!

  • @krishlapatra424
    @krishlapatra424 4 роки тому +1

    Really nice ... So clear concept.... Thank you professor Dave

  • @jocelyneavila6870
    @jocelyneavila6870 3 роки тому +1

    Thank you for the subtitles in English! It makes it much easier to follow-up.

  • @chroma9848
    @chroma9848 4 роки тому +9

    You're an excellent teacher, you truly are. I survived 1st year of engineering with your help. It would be nice if you can make videos on differential equations 😅

  • @melontusk7358
    @melontusk7358 3 роки тому +2

    I've finally done it. Thanks for your help, my good sir. I'm a lot more confident now.

  • @sine4859
    @sine4859 2 роки тому +2

    wow i didnt expect integrals to have this much depth to them... how can you not love math, omg
    great video btw :)

  • @md.azmiribneislam6885
    @md.azmiribneislam6885 4 роки тому

    Nice work... You deserve a big big big thanks... Go ahead Dave brother

  • @mavlonkarlsefni
    @mavlonkarlsefni Місяць тому

    I have a test tomorrow, and your video really helped me to understand integration more deeply. Thanks from Russia!

  • @mkpr757
    @mkpr757 2 роки тому

    A video masterpiece. Grateful for the illustrations, painted a clearer picture in my mind...

  • @tanishq1026
    @tanishq1026 2 роки тому +1

    Thank you so much! I really appreciate this as we don't get taught a lot of concepts and underlying principles in math, so this just makes the subject so much more interesting. :)

  • @huijiang3051
    @huijiang3051 2 роки тому

    Thanks Dave, you are a wonderful professor!👍

  • @dalibormaksimovic6399
    @dalibormaksimovic6399 Рік тому

    Thats the most outstanding explanation I ever got. Thank you so much!

  • @andreacondello
    @andreacondello 2 роки тому

    that is amazing how clear you was

  • @werkatfischer3183
    @werkatfischer3183 2 роки тому

    This is probably the best that this video could possibly have been made.

  • @sauravkr.mahato
    @sauravkr.mahato 2 роки тому

    Great Visualization of the figure formed by double integration
    Loved it !!

  • @coop_the_troop
    @coop_the_troop 3 роки тому +8

    Man I’m trying to learn first calculus, I was recommended this from a friend in the math field to help, it seems a bit to daunting, I wish I was I just good at math and actually understood what he is talking about most of the time

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  3 роки тому +14

      Start the calculus playlist from the very beginning and all will make sense!

  • @ndereratjijahura2048
    @ndereratjijahura2048 2 роки тому

    Thanks so much for a clear presentation.

  • @leedsoldat4189
    @leedsoldat4189 Місяць тому

    A learner from Tanzania,🤝you are a good teacher ❤

  • @user-fo8cu6ef5y
    @user-fo8cu6ef5y 10 місяців тому +1

    You're the E of the mc²! Great lecture. Congrats.

  • @thabolikotsi5765
    @thabolikotsi5765 4 роки тому +1

    awesome vid thanks im a fresher ive jusst started self learning ths topic ths will help wth understanding

  • @mohamedamr6228
    @mohamedamr6228 3 роки тому

    You are a GENIUS...Such a relief to finally understand the bounds depending on variables... thanks for your hardwork really appreciate it

    • @dellpi3911
      @dellpi3911 3 роки тому

      ua-cam.com/video/IangXACFW48/v-deo.html

  • @sudharakafernando4391
    @sudharakafernando4391 3 роки тому

    Professor Dave is the best...thank you very much!!!!

  • @annea1537
    @annea1537 4 місяці тому

    Danke sehr!!!
    🎊 beste Erklärung! Mit Abbildungen, klar und deutlich.
    ❤❤❤❤❤

  • @nosirrahonline1225
    @nosirrahonline1225 Рік тому

    Oh my god, thank you so much for this video. The videos that I get for my class gave me an example where both y and x's bounds were 1 so I didn't understand how she was doing it.

  • @someone________2502
    @someone________2502 2 роки тому +1

    Great video. Even though I only did high school calculus I could still follow what he is saying.

  • @encinaallaineharleya.8586
    @encinaallaineharleya.8586 Рік тому

    We have a calc quiz tomorrow and this video sure helps, Thanks!

  • @amaizasafdar9401
    @amaizasafdar9401 3 роки тому

    no word to explain your efforts may God reward this

  • @darkwing2924
    @darkwing2924 2 роки тому

    Thanks for making calculus fun and interesting

  • @Zephyr-tg9hu
    @Zephyr-tg9hu 4 роки тому +2

    Thank you so much, Dave! You are and always have been a lifesaver.

  • @TTeach22
    @TTeach22 Рік тому

    Great thought and too clear fellow style, I apricate your way of explains

  • @fightinggod03
    @fightinggod03 2 роки тому

    whenever my dad checks up on me if im doing work, i just pull up your videos and he doesnt question it! thank you :D

  • @NoctuaStrigiformes
    @NoctuaStrigiformes 4 роки тому +2

    Integrals are tight. You made it look super easy, barely an inconvenience.

  • @aceflamez00
    @aceflamez00 4 роки тому +6

    Wow that was easier then expected. Thank you for explaining it well.

  • @alexanderkaiser89
    @alexanderkaiser89 2 роки тому +6

    Hi Professor Dave.
    I have a request that you may find interesting or not, it’s a mathematical one. I have always found it hard to understand “Inter-universal Teichmüller theory”, “The Collatz Conjecture”, and “The Birch and Swinnerton-Dyer Conjecture”. If you would make a video on one of these topics that would really help 😊
    I’m studying a Master’s in mathematics in Denmark. I’m sorry for my English, I’m not mothertongue in English.
    Btw, I love your content.

  • @ItIsMe167
    @ItIsMe167 4 роки тому

    Good Job, Thanks for Sharing

  • @pawanmarahatta5749
    @pawanmarahatta5749 16 днів тому

    blessings upon you, Dave.

  • @millieh3179
    @millieh3179 4 роки тому +100

    Can you do a video on Green's, Stokes' and Gauss' Theorems?

    • @Universities_Reels
      @Universities_Reels 4 роки тому +4

      Could you send me notes of divergence theorem ?

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  4 роки тому +81

      Millie all three of those are filmed, animated, uploaded, and to be released very soon!

    • @GeoRaphaelMichael
      @GeoRaphaelMichael 3 роки тому +1

      @lulu , your wicked tactics to paint real Christians ain't gonna work, people like you are the reason muslims conflate legitimate love lead criticism from people like David Wood and Robert Spencer with hatred from people like you and richard spencer.

    • @awesomecodeyay8382
      @awesomecodeyay8382 3 роки тому +2

      20UPH512_Geo Raphael Michael
      What was lulu’s comment about?

    • @ivoryas1696
      @ivoryas1696 7 місяців тому

      ​@@GeoRaphaelMichael
      *_Bruh, what_*

  • @ejticomon9603
    @ejticomon9603 Рік тому +5

    Why is the y integral from x^2 to 2x and not 2x to x^2?

  • @virajpatel2121
    @virajpatel2121 2 роки тому

    Sir you are awesome ,I love your explanation method. 😇😇😇

  • @christianb4679
    @christianb4679 4 роки тому +4

    Thanks so much! I never understood this in my Engineering lectures, now it makes sense.

    • @os9458
      @os9458 4 роки тому +1

      Hi Rosal.can I know is this thing involve I'm grade 12 or higher grade .Because I'm going to do engineering too. Currently grade 12

    • @christianb4679
      @christianb4679 4 роки тому +1

      OsJ I’m not sure, I studied this in university.

  • @jacobridley8156
    @jacobridley8156 Рік тому

    so helpful cheers Dave

  • @hexagor5140
    @hexagor5140 Місяць тому

    Thank you sm genuinely

  • @kaymoneyalottoww4828
    @kaymoneyalottoww4828 3 місяці тому

    cool teacher, straight to the point

  • @Jack-lp4jd
    @Jack-lp4jd Рік тому +2

    Best explanation around. Though im still struggling to understand how taking the integral of the x-y plane in two different ways gives volume. So the area under the curve given from the first integral just happens to also equal the volume?

  • @thefatcat1997
    @thefatcat1997 4 роки тому +5

    I wish i had u as my teacher during my btech...

  • @kamalnath4606
    @kamalnath4606 6 місяців тому +1

    love you professor dave

  • @bryanwharton6692
    @bryanwharton6692 4 роки тому +26

    “Performing multiple integrations is not all that daunting, on the SURFACE!!” Haha

  • @henryy6918
    @henryy6918 4 роки тому

    Wonderful video.

  • @prateek3828
    @prateek3828 Рік тому

    I thank you dear sir for mentoring me . 🙏

  • @pankajpokhrel2463
    @pankajpokhrel2463 4 роки тому

    Very well explained..

  • @adristimaulidafauzi4418
    @adristimaulidafauzi4418 3 роки тому +1

    Finally I understand the sense behind these

  • @itsme.01
    @itsme.01 8 місяців тому +1

    In the first comprehension, when we move from 2 to 3 in x,then y=x+1 is lower to 2x . Why we consider here limit in y from 2x to (x+1)?

  • @azadprasad856
    @azadprasad856 3 роки тому

    He does know all about science stuff......... professor Dave Explains ❤️❤️❤️🔥🔥🔥. I Love this😎

  • @astroflexx82
    @astroflexx82 Рік тому

    Amazing video!

  • @mohitchaurasia7181
    @mohitchaurasia7181 4 роки тому +4

    💥👌Nice explanation 💥👌☺️🤗

  • @HorizonSpeed26
    @HorizonSpeed26 4 роки тому

    Thanks very useful and understandable

  • @kerryloh5285
    @kerryloh5285 6 місяців тому

    Nice explaination

  • @aloischipfurutse5079
    @aloischipfurutse5079 3 роки тому +10

    I still don't understand why someone can dislike a video like this :( You are incredible!

    • @dellpi3911
      @dellpi3911 3 роки тому

      ua-cam.com/video/IangXACFW48/v-deo.html

  • @didyk3574
    @didyk3574 4 роки тому +2

    Hey dave can you graph this function in 3D f(x,y)=xy/(x^2-y^2) around the point(0,0)

  • @jainyshah3000
    @jainyshah3000 4 роки тому +1

    Brilliant! Thanks :)

  • @JorgetePanete
    @JorgetePanete 4 роки тому +3

    1:37 I think there are counterexamples to that statement, but it works in general.

  • @chandraprakash934
    @chandraprakash934 4 роки тому

    very good , thanks !

  • @mayashomarieh7941
    @mayashomarieh7941 Рік тому

    Thank you so much

  • @freezinfire
    @freezinfire 2 роки тому

    Thank you very much.

  • @deltaexplorer47
    @deltaexplorer47 4 роки тому

    WOW !! THANK YOU VERY VERY MUCH !!

  • @musthafamb1757
    @musthafamb1757 3 роки тому

    Great teacher

  • @nirodlowe1615
    @nirodlowe1615 Рік тому

    Just keep it up professor!🥳🥳🥳

  • @taladiv3415
    @taladiv3415 3 роки тому

    Dave the man!

  • @kaluvanhariharan4256
    @kaluvanhariharan4256 11 місяців тому

    Highly informative lecture. Thanks Professor . In 7.31 , how did you the get function f(x,y)? will you please explain?

  • @TemplarX2001
    @TemplarX2001 4 роки тому +3

    annnnnnnnnnnnnnd you have a new sub/ bingewatcher

  • @9silentufo9
    @9silentufo9 4 роки тому

    Great video

  • @eskayML
    @eskayML 11 місяців тому +1

    I have a question please
    For the upper and lower bounds isn't the x² greater than 2x and why didn't it get placed at the upper bound instead?.

  • @mohammadtorikh
    @mohammadtorikh Рік тому

    Thank you sir

  • @jackrubin6303
    @jackrubin6303 3 роки тому

    If you look at f(x,y) = 1+ 4xy example, if you just look at solid by itself and compute volume without using complex integration, for x = 1 (1-0), y = 2, (3-1), and z = 1 + (4*1*2) = 9, I get a volume of 1*2*9=18. Where did I got wrong?

  • @STKeTcH
    @STKeTcH 3 роки тому

    You the man, man!

  • @danielvolinski8319
    @danielvolinski8319 2 роки тому +1

    14:30 The first example on the Checking comprehension is wrong: the internal integral boundaries should be from x+1 to 2x

  • @christosgolsouzidis1286
    @christosgolsouzidis1286 4 роки тому +14

    I thought that double integrals give the area of the surface of a function and triple integrals the volume of a function respectively

    • @tzonic8655
      @tzonic8655 3 роки тому

      Και εγώ ρε φίλε,έτσι δεν λέει και ο γκαρουτσος? 😂

  • @student_0224
    @student_0224 3 роки тому

    Thanks a lot sir....

  • @paulgbago4586
    @paulgbago4586 4 роки тому +4

    hello can explain how you take x^2 as the lowest value for a integral and another integral.
    what makes them the upper value on y and lowest value on x ?can you make it more clear cause i tried to find why but still cant find out .
    At first i thought it was cause the 2x function was above the x^2 from 0 to 2.
    thanks you

    • @yuel.5013
      @yuel.5013 4 роки тому +1

      You're right, depends on the sign. Solve sqrt(y) >= y/2, it's true on [0; 4].

  • @pakshah5449
    @pakshah5449 4 місяці тому

    Thanks Great Video

  • @ramuganesan
    @ramuganesan 2 роки тому +1

    at 07:12 , how do you say that y runs from the lower curve to upper curve? sir i cant understand that point

  • @SMNAviation
    @SMNAviation 3 роки тому +2

    I consider the view count on this an insult. And an even greater one, that 52 people dare dislike it. Dave, your videos are amazing.

  • @AmanT241
    @AmanT241 2 роки тому

    oh men i wish i knew you back when i was taking Applied maths 2 in college

  • @extremelearning3113
    @extremelearning3113 2 роки тому

    It's an excellent explation.

  • @4tytude
    @4tytude 3 роки тому

    hi professor dave, in 4:00 you said 10 is the volume under that given example surface, why does it considered "under" not "above"?