Calculating the Volume of a Solid of Revolution by Integration

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  • Опубліковано 28 вер 2024

КОМЕНТАРІ • 290

  • @johnryan7661
    @johnryan7661 Рік тому +45

    That bit where we all of the sudden derive the formula for a sphere’s volume via integration has to be one of the coolest things I’ve ever seen.

  • @vikvak1275
    @vikvak1275 4 роки тому +785

    this is 10 times better explained than in my math book

    • @digitbvj5
      @digitbvj5 4 роки тому +32

      As a math teacher, I agree with this! Haha

    • @jamesmaybury7452
      @jamesmaybury7452 3 роки тому +11

      Does that mean that it takes 1/10 the time to learn the same amount, or that you now know how to solve 10 times the number of problems. The idea that it works out as an integer rather than say, 9.841 times better is intriguing. . . . .Perhaps I’m taking this too literally.

    • @gambu4810
      @gambu4810 3 роки тому +2

      This is so true and frustrating

    • @memorynkhoma7964
      @memorynkhoma7964 3 роки тому +1

      Text book? If so what book are/were you using

    • @PoojaSharma015
      @PoojaSharma015 2 роки тому +1

      Change it 1000*
      🙌🏻🙌🏻

  • @edmonlee9311
    @edmonlee9311 5 років тому +13

    By far the best physics and math tutorials on youtube. Some explanations are kept so simple to understand, its better than going to class

  • @scitalks8286
    @scitalks8286 2 роки тому +8

    Thanks Professor Dave, you're a live saver. I didn't understand anything about this topic from my textbook but your video explained everything soooo clearly!!!!

  • @brettferro
    @brettferro 7 місяців тому

    This account is AMAZING. He gets right to the point in every video and it makes sense.

  • @bipedalnarwhal277
    @bipedalnarwhal277 3 роки тому +4

    This explanation saved me for my calc exam!

  • @ДиляраРузиева-й7к

    Thanks a million for such amazingly helpful videos as I don't understand anything on the lectures and thanks to u I've survived for the last 3 years studying it😂😂😂😂😂😂😂😂❤❤❤❤❤❤

  • @vytg706
    @vytg706 2 роки тому +1

    thank you so much, you will never know how grateful i am for this

  • @zenicv
    @zenicv 2 роки тому +6

    Thank you professor, this was an excellent supplement for my integration studies

  • @sergekamga4512
    @sergekamga4512 2 роки тому +1

    Wow. The explanation is superb

  • @idealmathsdeosir9308
    @idealmathsdeosir9308 3 роки тому +1

    Excellent Sir

  • @Charky32
    @Charky32 Рік тому +1

    what a brilliant explanation

  • @charlessandoz2522
    @charlessandoz2522 2 роки тому +2

    Not gonna fail my exam tomorrow anymore, thank you!

  • @JesusMartinez-zu3xl
    @JesusMartinez-zu3xl 2 роки тому +1

    you explained this in 11 minutes compared to two hours of lecture. wow!

  • @AbC-bj3gs
    @AbC-bj3gs Рік тому +1

    an outstanding video, a masterpiece

  • @jn2869
    @jn2869 3 роки тому +1

    For the X, why did he make it x^2, is it because it’s the outer radius?

  • @jeanpierremattei4073
    @jeanpierremattei4073 Рік тому +1

    Thank again for this very clear video

  • @ojaspatil2094
    @ojaspatil2094 2 роки тому

    genuinely so good, ty!

  • @elamvaluthis7268
    @elamvaluthis7268 4 роки тому

    Nice explanation

  • @Parmesanz
    @Parmesanz 3 роки тому +2

    Thank you a lot, Professor Dave!

  • @JayLegazpi
    @JayLegazpi 4 місяці тому

    Very well done sir! Thank you!

  • @lunatickiller1494
    @lunatickiller1494 2 роки тому

    Im in love with that intro

  • @iridium8562
    @iridium8562 4 роки тому +11

    9:44
    « And figure out what the ff-«
    Literally thought he is going to drop an f bomb xD

  • @ACTION646
    @ACTION646 3 роки тому +1

    At around 2:17 you say But we want this in terms of the radius of the sphere, because that is unchanging. I didn't understand that part. Can't we integrate with y and dy in that part.

  • @songthanh896
    @songthanh896 3 роки тому +1

    3:57 wow easier than what my professor taught years ago

  • @pied6
    @pied6 5 місяців тому

    How can y be the radius in the formula A= pi * y^2,when y is only the radius at the instance where x=0 ?

  • @shibajeesarkar7846
    @shibajeesarkar7846 3 роки тому +1

    Thanks a lot. Very well explained. ❤️

  • @klairehoang667
    @klairehoang667 4 роки тому +2

    Can anyone please explain to me the role of x when he calculates the volume of the sphere? Does x play any role at all or is it just there?

  • @MarshaTembo
    @MarshaTembo 4 місяці тому

    Good PROFF!!!!👏

  • @rizkaapriliani1630
    @rizkaapriliani1630 2 роки тому +1

    sir i wanna ask if there is no bounds and the curve goes to infinity, what should i do? should i just integrate it from 0 to 1??

  • @Free_again..
    @Free_again.. 4 роки тому +1

    amazinggggg
    realllyyy helpful keep it up

  • @mrxy8521
    @mrxy8521 4 роки тому +1

    Man this is real easy.

  • @dylangabriel2703
    @dylangabriel2703 11 місяців тому

    Is it possible to do this with very irregular shapes, where it’s integrating x^2 and y^2

  • @MikiSiguriči1389
    @MikiSiguriči1389 2 роки тому

    first watched your flat earth series, now this, good job keep it up :D cheers from Serbia

  • @batteryjuicy4231
    @batteryjuicy4231 9 місяців тому +1

    my math book has some (dy/dx)^2 + 1 all under a root bullshit. This was very helpful!!!!!!!

  • @pubgkidshooter
    @pubgkidshooter Рік тому +2

    which software is used in this video like like rotating a curve along xaxis and make a 3D shape to find volume??

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  Рік тому +5

      I did in after effects and it took freaking forever. It’s not 3D I just animated solids to look that way.

  • @nayelnayel865
    @nayelnayel865 2 роки тому

    5:31 why is it square root of x? I don't get it

  • @navagharkiran5769
    @navagharkiran5769 5 років тому +2

    units will be in cubic ?

  • @pikachudemsy9751
    @pikachudemsy9751 5 місяців тому +1

    What app or website did you use to model this

  • @officialjuicy
    @officialjuicy 4 роки тому

    best video ever

  • @asmimiramli9634
    @asmimiramli9634 2 роки тому +1

    How to make this kind of animation? Anyone knows what software to graph this. Help :")

  • @manishshah2424
    @manishshah2424 5 років тому +1

    Can you show me the animation of the revolution of the last question.

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  5 років тому +6

      those little 1-2 second animations took me over an hour each, so i won't be doing more of those anytime soon!

    • @manishshah2424
      @manishshah2424 5 років тому +1

      Can you help me on this:Determine the volume of the solid generated by revolving the plane area bounded by the curve y^(2)=4x and x=4 about the line x=4.(Small Hint will work).Thanx For the reply btw.

  • @sherazanwar5783
    @sherazanwar5783 3 роки тому

    Nice

  • @laks318
    @laks318 6 місяців тому

    How fabulous is this...❤❤❤🥹🥹🥹🥹thank you life saver...

  • @colonizingfear
    @colonizingfear Рік тому +33

    Nothing better than Jesus teaching me how to do calculus before an exam

  • @aryanshahu6167
    @aryanshahu6167 3 роки тому +75

    It’s all fun and games until your teacher gives you this in conics

  • @alisont4344
    @alisont4344 4 роки тому +192

    you're honestly such a livesaver. i feel so lucky to have stumbled across one of your videos! keep it up man you're helping alot of people with these videos!

  • @samk6042
    @samk6042 5 років тому +182

    Our math teacher made us watch u in class xD everyone cracked up at ur intro

    • @harshjoshi4008
      @harshjoshi4008 4 роки тому +9

      Our teacher made us watch it in BTech......

    • @creativeink4407
      @creativeink4407 3 роки тому

      our teacher made us wach him in level physics

  • @oishikachaudhury3718
    @oishikachaudhury3718 5 років тому +69

    This is such an amazing video. Most professors miss out on actually helping us visualise like you just did.

  • @Melvorgazh
    @Melvorgazh 2 роки тому +2

    @Professor Dave Explains
    Hello Professor,
    I have been looking for blueprints for a 10-gores bulbous hot air balloon on the Internet and found zip.
    So I was wondering about designing one meself.
    Only I need the mathematical formulas and a few advanced Geometry lessons.
    Would you have a video that could help me?
    Something oriented with curves and volumes...
    Regards,
    Thomas from Brussels, Belgia.

  • @jasontodd1419
    @jasontodd1419 6 років тому +104

    You explain everything so well and clearly , you're videos are so awesome !! Thank you so so sorry much , and please keep it up , I'd donate if I had the money!! 😊

    • @arnabnath6601
      @arnabnath6601 5 років тому +11

      What is thank you so so sorry much 😂😂😂😂

    • @devakinandan7659
      @devakinandan7659 5 років тому +5

      @@arnabnath6601 maybe auto correct probe, XD

    • @arnabnath6601
      @arnabnath6601 5 років тому +2

      @@devakinandan7659 was just kidding 😁😁 anyway thank you 😊😊

    • @devakinandan7659
      @devakinandan7659 5 років тому +2

      @@arnabnath6601 no probs :-)

  • @Noname-bm3nx
    @Noname-bm3nx 2 роки тому +1

    He is the jesus of math

  • @FlyingscotsmanINC
    @FlyingscotsmanINC 4 роки тому +29

    The dislikes are from the math professors that could not do as good of a job of explaining these concepts as you did.
    In all seriousness, these videos are amazing and I will definitely be visiting them frequently

  • @SXLTY._.
    @SXLTY._. Рік тому +1

    I got a question so how do we know like on the disk method how high the function is for example let’s say we got root x as a function right,
    So we know how long it goes by the x axis let’s just say 0-8 but what would the y axis be cause we don’t plug it in the formula

  • @hieuhandbalance
    @hieuhandbalance 4 роки тому +16

    Thanks you Dave, your lesson is so fun and easy to learn, finally I can calculate the volume of sold of revolution through integral, math is sooo interesting, love your video so much !! (cant remember those time study math in my school, bored af :( )

  • @prori5297
    @prori5297 Рік тому +7

    Can I cut some parts of your video about 3D shape to add them in my presentation at class? I will share your channel to my classmates. Your video is so helpful

  • @alexanderkaiser89
    @alexanderkaiser89 2 роки тому +12

    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.

    • @vanskis7618
      @vanskis7618 2 роки тому +2

      Your English is better than most native speakers xD. No need to apologize.

    • @alexanderkaiser89
      @alexanderkaiser89 2 роки тому +1

      @@vanskis7618 Lol, thanks. I never did ‘perfect’ in school when I had language of any forms…

  • @AdzzVR
    @AdzzVR 2 роки тому +1

    I got lost @3:45, why did the x disapear, and r^3/3 replaced x^3/3 and power of r increase? If I am following right, did you sub r in for x since you are evaluating at the limits?

  • @harshpreetsingh1228
    @harshpreetsingh1228 3 роки тому +14

    This is the best explanation I've found on Solids of Revolution, thanks!!

  • @deliveringIdeas
    @deliveringIdeas 2 роки тому +1

    Dave, I am in love with you. Thanks.

  • @talesara74
    @talesara74 4 роки тому +3

    If I try to replace y by R Sin(theeta) and try to integrate from angle o to pai/2..I dont get the desired result. Not sure what is wrong I m doing here. So my integeral is sum (pai R^2 Sin^2theeta delta dheta) from 0 to pai/2.

  • @elamvaluthis7268
    @elamvaluthis7268 Рік тому +2

    Very very nice explanation 👍👍👍.

  • @thebreadst
    @thebreadst 3 роки тому +1

    Is this the disc method or the shell method?

  • @loicgeeraerts
    @loicgeeraerts 3 роки тому

    Ce qui serait bien, c'est d'aller voir comment les pays qui réussissent s'y prennent afin d'éviter de toujours revenir au passé, à l'école à l'ancienne et à la règle de trois, qui cela dit en passant n'est plus enseignée dans certains pays qui réussissent très bien les tests internationaux. Tant que la France ne sortira pas ce de paradigme, les choses ne cesseront pas de se dégrader.

  • @awesome7732
    @awesome7732 4 роки тому +9

    dude the 3 calc professors at my school suck so much but you are amazing. you actually explain why things are the way they are instead of just writing long equations on the board and skipping steps

  • @EzzTurky
    @EzzTurky Рік тому +1

    erika and zara and annabelle

  • @neelg7736
    @neelg7736 3 роки тому +7

    This is genuinely the best video I have ever watched over the subject. Thank you so much!! a literal lifesaver

  • @fredrickongowe4155
    @fredrickongowe4155 5 років тому +8

    At last i have understood what goes on around solids of revolution by integration method, kudos Prof. Dave

  • @EMANUELITAMBU-y7j
    @EMANUELITAMBU-y7j 8 місяців тому +2

    I come from Tanzania. I use many books for understanding but I look it is so difficult to me but through your teaching I have started nice understands about calculation of volume of a solid of revolution, so thanks

  • @ankitdhaker111
    @ankitdhaker111 4 роки тому +7

    this is the way to understand concepts. thanku

  • @davidm3210
    @davidm3210 4 роки тому +8

    The Rembrandt of math videos - truly exceptional!

  • @EMANUELITAMBU-y7j
    @EMANUELITAMBU-y7j 8 місяців тому +2

    Professor Dave may God protect you continually, you are helping us more than our teachers. So thanks🙏🙏

  • @zalak3855
    @zalak3855 2 роки тому +1

    God just 3 min and my doubt became crystal clear ❤

  • @Mr.Paheli.131
    @Mr.Paheli.131 Рік тому +2

    I LOVE YOUR EXPLANATION SIR

  • @gin1954
    @gin1954 Рік тому +2

    Sir explained 100x better than out lecturer

  • @dilantunc7428
    @dilantunc7428 5 років тому +12

    sağol reis sen anlatana kadar anlayamamıştık eyvallah

  • @nightmare5022
    @nightmare5022 2 роки тому +1

    this is the 10th video I watched and finally washer method clicked thank you dude your saving my AP Calc grade 😭

  • @barshapant9983
    @barshapant9983 3 роки тому +5

    What a explanation ! I am impressed by your process of teaching.

  • @HiiImChris
    @HiiImChris 2 роки тому

    Holy shit you are a god at generalizing a concept for first timers. Very wonderful, the concept is most important because practice inevitably can be done to solidify said concepts

  • @azfa9338
    @azfa9338 4 роки тому +7

    thank u so much for this i literally forgot how to find volume using integration meanwhile i have an upcoming mock exams for my AS levels tmr, you saved my life! hahaha

  • @muhammadaashir6931
    @muhammadaashir6931 2 роки тому +1

    Loved the start part 👍😂😂

  • @itsvollx9684
    @itsvollx9684 3 роки тому +1

    Professor Dave
    can you explain why everyone uses this Math Alien Language I got no way I can understand it

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  3 роки тому

      Start earlier in the mathematics series and pick up what you're missing!

  • @happyfamily6866
    @happyfamily6866 3 роки тому +1

    I'm from India , really very helpful this explanation with animation

  • @andersonchen7501
    @andersonchen7501 2 роки тому +1

    after this video you made me fall in love with the subject I used to hate the most. thank you

  • @kaileagoff
    @kaileagoff 3 роки тому +1

    omg this makes 100X more sense, THANK YOU SO MUCH!!!!!

  • @mathematicaa6876
    @mathematicaa6876 4 роки тому +2

    Kindly could you tell me what is the used program to make such a great video

  • @coreylevy7
    @coreylevy7 4 роки тому +2

    I have an AP Calc BC online test in 38 mins, I’m learning this now... please pray for me

    • @coreylevy7
      @coreylevy7 4 роки тому

      @@ggeorge02 perfect score, easy dubs

  • @leenjundi3811
    @leenjundi3811 Рік тому +1

    thankk uucramming this midterm n this helped

  • @thefalcica8340
    @thefalcica8340 4 роки тому +3

    Hi professor Dave, there is a question I don’t understand how can I know if it’s disc or disc hole or shell????? I am really confused please help

    • @garrydelgado6260
      @garrydelgado6260 2 роки тому

      I know it's too late but to answer your question, as you can see @7:19, a washer (disc hole) if it is an area enclosed between a curved and a line rotated to the x-axis.

  • @Jasmine-ww7jl
    @Jasmine-ww7jl 3 роки тому +5

    WHAT THIS IS LIKE A WHOLE NEW SIDE TO EVERYTHING IVE NEVER KNOWN THANK YOU

  • @stianclar
    @stianclar 5 років тому +3

    I've learned it without really understanding the logic and proof behind it. If only would somebody had explained me this way, Jeez. You're amazing!

    • @38Fanda
      @38Fanda 5 років тому +1

      explaining things?? you're asking too much from regular math teachers!

  • @justinernest2363
    @justinernest2363 3 роки тому +1

    Great video🤩but please consider leaving the answers to the compression as it is quite useless not to🥺

  • @subodhKumar-bx1sm
    @subodhKumar-bx1sm 4 роки тому +1

    The valume generated by revolving the area bounded by y2=8x and the line x=2 about y axis is ???? Sir please solve

  • @yaoyaoxiao6637
    @yaoyaoxiao6637 4 роки тому +2

    for the sphere, since it is dx cross section, shouldnt it be the y values to integrate? which nevertheless doesnt matter since it would still be -r,r but thoughts?

  • @z.r1999
    @z.r1999 3 роки тому +1

    1st time on this channel and cannot go back without Subscribing this channel 😍

  • @aashsyed1277
    @aashsyed1277 3 роки тому +3

    This is a million million million million times better than any other lecture.

  • @zatak3689
    @zatak3689 2 роки тому +1

    Hello I have a question, when we integrate we get the area between the limits of the 2D region. So why can't we multiply the area with 2pi to get the volume of the revolution? Why do we multiply with pi instead of 2pi? Help will be much appreciated. Thanks

  • @stravaoritdidnthappen
    @stravaoritdidnthappen 2 роки тому

    Thanks man! Rad video haha I watched it with a bunch of other people and had so much fun haha. THIS VIDEO WAS SO MUCH BETTER THAN MY FUCKING STUPID TEACHER WHOM I WOULD MAIM WITH A ROCK (humongous rock btw lol) AT THE DROP OF A HAT. thanks again :^)

  • @kenjifujiwara9307
    @kenjifujiwara9307 3 роки тому +4

    Great explanation and quality video! I appreciate it!!!

  • @gvhu3542
    @gvhu3542 4 роки тому +2

    Thank you very much...it was really helpful