Calculating the Volume of a Solid of Revolution by Integration

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  • เผยแพร่เมื่อ 31 ม.ค. 2025

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  • @johnryan7661
    @johnryan7661 2 ปีที่แล้ว +83

    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 ปีที่แล้ว +854

    this is 10 times better explained than in my math book

    • @digitbvj5
      @digitbvj5 4 ปีที่แล้ว +34

      As a math teacher, I agree with this! Haha

    • @jamesmaybury7452
      @jamesmaybury7452 4 ปีที่แล้ว +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 ปีที่แล้ว +2

      This is so true and frustrating

    • @memorynkhoma7964
      @memorynkhoma7964 3 ปีที่แล้ว +1

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

    • @PoojaSharma015
      @PoojaSharma015 3 ปีที่แล้ว +1

      Change it 1000*
      🙌🏻🙌🏻

  • @alisont4344
    @alisont4344 4 ปีที่แล้ว +200

    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!

  • @oishikachaudhury3718
    @oishikachaudhury3718 5 ปีที่แล้ว +75

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

  • @awesome7732
    @awesome7732 5 ปีที่แล้ว +12

    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

  • @FlyingscotsmanINC
    @FlyingscotsmanINC 4 ปีที่แล้ว +35

    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

  • @aryanshahu6167
    @aryanshahu6167 3 ปีที่แล้ว +87

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

  • @edmonlee9311
    @edmonlee9311 5 ปีที่แล้ว +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

  • @aashsyed1277
    @aashsyed1277 3 ปีที่แล้ว +5

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

  • @ayhamyahya6939
    @ayhamyahya6939 4 ปีที่แล้ว +7

    There is an obvious reason why your explanation is unique. You actually make us visualize the actual damn question. Much love

  • @samk6042
    @samk6042 5 ปีที่แล้ว +185

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

    • @harshjoshi4008
      @harshjoshi4008 4 ปีที่แล้ว +10

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

    • @creativeink4407
      @creativeink4407 3 ปีที่แล้ว +1

      our teacher made us wach him in level physics

  • @fredrickongowe4155
    @fredrickongowe4155 5 ปีที่แล้ว +8

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

  • @neelg7736
    @neelg7736 4 ปีที่แล้ว +7

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

  • @scitalks8286
    @scitalks8286 3 ปีที่แล้ว +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!!!!

  • @harshpreetsingh1228
    @harshpreetsingh1228 3 ปีที่แล้ว +14

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

  • @jeanpierremattei4073
    @jeanpierremattei4073 ปีที่แล้ว +1

    Thank again for this very clear video

  • @EMANUELITAMBU-y7j
    @EMANUELITAMBU-y7j ปีที่แล้ว +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

  • @flamingturkey7727
    @flamingturkey7727 7 หลายเดือนก่อน

    THANK YOU SO MUCH! AFTER 7 HOURS, YOU’RE THE FIRST PERSON TO EVEN MENTION AREAS ENCLOSED BY 2 FUNCTIONS.

  • @stianclar
    @stianclar 5 ปีที่แล้ว +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 ปีที่แล้ว +1

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

  • @colonizingfear
    @colonizingfear ปีที่แล้ว +45

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

    • @bri_420
      @bri_420 9 หลายเดือนก่อน +1

      crazy😭😭😭😭💀

    • @nithinsirimanne2924
      @nithinsirimanne2924 8 หลายเดือนก่อน

      JJ?

    • @Algebrainiac
      @Algebrainiac 6 วันที่ผ่านมา

      🤣🤣🤣🤣

  • @cosmicnomad8575
    @cosmicnomad8575 2 ปีที่แล้ว +2

    There’s something so beautiful and elegant about this concept! Great video as always!

  • @EMANUELITAMBU-y7j
    @EMANUELITAMBU-y7j ปีที่แล้ว +2

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

  • @Jasmine-ww7jl
    @Jasmine-ww7jl 4 ปีที่แล้ว +5

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

  • @brettferro
    @brettferro 11 หลายเดือนก่อน

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

  • @jasontodd1419
    @jasontodd1419 6 ปีที่แล้ว +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 ปีที่แล้ว +11

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

    • @devakinandan7659
      @devakinandan7659 5 ปีที่แล้ว +5

      @@arnabnath6601 maybe auto correct probe, XD

    • @arnabnath6601
      @arnabnath6601 5 ปีที่แล้ว +2

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

    • @devakinandan7659
      @devakinandan7659 5 ปีที่แล้ว +2

      @@arnabnath6601 no probs :-)

  • @happytobeme5011
    @happytobeme5011 2 หลายเดือนก่อน +1

    Such an amazing video! Really well explained, i have a presentation tomorrow on this topic and i could not go anywhere but watch and learn from you, it is such a life saver ❤❤❤❤❤

  • @hieuhandbalance
    @hieuhandbalance 4 ปีที่แล้ว +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 :( )

  • @detroitpistonsplayoffs
    @detroitpistonsplayoffs 2 ปีที่แล้ว +1

    Awesome video, My head was spinning trying to make sense of this from my text book. But then again, it only makes sense to learn about volume via a medium where 3 dimensions can be better represented, such as a video, rather than a piece of paper or white board. Thanks!

  • @azfa9338
    @azfa9338 5 ปีที่แล้ว +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

  • @arunmishra4348
    @arunmishra4348 4 ปีที่แล้ว +1

    Out standing explanation sir
    I have never seen such type of explanation in my life.
    Accept my heartily congratulation from bottom of my heart for such excellent explanation.

  • @PoojaSharma015
    @PoojaSharma015 3 ปีที่แล้ว +1

    We genuinely appreciate and support your work ❤️.

  • @andersonchen7501
    @andersonchen7501 2 ปีที่แล้ว +1

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

  • @gin1954
    @gin1954 2 ปีที่แล้ว +2

    Sir explained 100x better than out lecturer

  • @PookieAndAnnie
    @PookieAndAnnie 21 วันที่ผ่านมา

    I just realized we need video textbooks 4:48
    I need animated hard copy texts
    Thank you Prof Dave

  • @anabarcenas9893
    @anabarcenas9893 ปีที่แล้ว

    These visuals are 10/10 and you are too! I wish ALL teachers were like you!

  • @benno19891
    @benno19891 16 วันที่ผ่านมา

    Great content. I am a visual and verbal learner so these videos are exponentially helpful! Thanks.

  • @bipedalnarwhal277
    @bipedalnarwhal277 3 ปีที่แล้ว +4

    This explanation saved me for my calc exam!

  • @ДиляраРузиева-й7к
    @ДиляраРузиева-й7к ปีที่แล้ว +1

    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😂😂😂😂😂😂😂😂❤❤❤❤❤❤

  • @punditgi
    @punditgi 3 ปีที่แล้ว +3

    Beautiful explanation and graphics make the concepts crystal clear!

    • @oksowhat
      @oksowhat 3 ปีที่แล้ว

      u doing engineering too?

  • @vytg706
    @vytg706 3 ปีที่แล้ว +1

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

  • @barshapant9983
    @barshapant9983 4 ปีที่แล้ว +5

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

  • @alexanderkaiser89
    @alexanderkaiser89 2 ปีที่แล้ว +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 ปีที่แล้ว +2

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

    • @alexanderkaiser89
      @alexanderkaiser89 2 ปีที่แล้ว +1

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

  • @HiiImChris
    @HiiImChris 3 ปีที่แล้ว

    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

  • @nightmare5022
    @nightmare5022 3 ปีที่แล้ว +1

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

  • @Aang_111
    @Aang_111 5 ปีที่แล้ว +7

    this is the way to understand concepts. thanku

  • @zenicv
    @zenicv 3 ปีที่แล้ว +6

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

  • @canyonero3654
    @canyonero3654 4 ปีที่แล้ว +1

    Tbh if i was a teacher i would always show these type of videos to class...cause it explains better than i would and majority of teachers

  • @oddlyperfectvids
    @oddlyperfectvids ปีที่แล้ว +1

    Now I'm actually beginning to understand calculus, thanks Prof Dave

  • @davidm3210
    @davidm3210 5 ปีที่แล้ว +8

    The Rembrandt of math videos - truly exceptional!

  • @happyfamily6866
    @happyfamily6866 4 ปีที่แล้ว +1

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

  • @JesusMartinez-zu3xl
    @JesusMartinez-zu3xl 3 ปีที่แล้ว +1

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

  • @Mr.Perfect.131
    @Mr.Perfect.131 ปีที่แล้ว +2

    I LOVE YOUR EXPLANATION SIR

  • @prori5297
    @prori5297 2 ปีที่แล้ว +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

  • @z.r1999
    @z.r1999 4 ปีที่แล้ว +1

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

  • @charlessandoz2522
    @charlessandoz2522 3 ปีที่แล้ว +2

    Not gonna fail my exam tomorrow anymore, thank you!

  • @anthonykirby9445
    @anthonykirby9445 3 ปีที่แล้ว +2

    So clear. Brilliant job.

  • @benedictespiritu1001
    @benedictespiritu1001 5 ปีที่แล้ว +2

    Great way and break down for people to understand the concept✊✊

  • @sergekamga4512
    @sergekamga4512 2 ปีที่แล้ว +1

    Wow. The explanation is superb

  • @elamvaluthis7268
    @elamvaluthis7268 2 ปีที่แล้ว +2

    Very very nice explanation 👍👍👍.

  • @nathanaelezan8905
    @nathanaelezan8905 5 ปีที่แล้ว +5

    even though this was made over a year ago, this was very helpful. Thank you.

  • @dilantunc7428
    @dilantunc7428 6 ปีที่แล้ว +12

    sağol reis sen anlatana kadar anlayamamıştık eyvallah

  • @Kiky_MedPhysicist
    @Kiky_MedPhysicist 5 หลายเดือนก่อน

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

  • @caomoletimoloi6565
    @caomoletimoloi6565 4 ปีที่แล้ว +1

    you are the best Prof Dave

  • @kenjifujiwara9307
    @kenjifujiwara9307 4 ปีที่แล้ว +4

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

  • @justinpeterson7643
    @justinpeterson7643 5 ปีที่แล้ว +2

    Properly good animations. Thank you.

  • @kaileagoff
    @kaileagoff 3 ปีที่แล้ว +1

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

  • @Charky32
    @Charky32 2 ปีที่แล้ว +1

    what a brilliant explanation

  • @AbC-bj3gs
    @AbC-bj3gs ปีที่แล้ว +1

    an outstanding video, a masterpiece

  • @giovannybarrera231
    @giovannybarrera231 3 วันที่ผ่านมา

    Watching this 6 years later while doing Homework. Thank you.

  • @slnuygn
    @slnuygn 3 ปีที่แล้ว +1

    You explained everything so clearly. You are awesome! I wish I had money so I could donate you

  • @shayangfkk7948
    @shayangfkk7948 4 ปีที่แล้ว +1

    every video professor dave makes us more in love with science . ;D

  • @HenrikMyrhaug
    @HenrikMyrhaug 6 ปีที่แล้ว +9

    Wow! I didn't understand anything until you explained!

  • @Joselo09111
    @Joselo09111 5 ปีที่แล้ว +5

    Thank you so much! Keep up the good content!

  • @hetbann
    @hetbann 5 ปีที่แล้ว +1

    best video on volumes ever

  • @7eguegueh499
    @7eguegueh499 ปีที่แล้ว

    You made me very happy! Thank you!

  • @coreylevy7
    @coreylevy7 4 ปีที่แล้ว +3

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

    • @coreylevy7
      @coreylevy7 4 ปีที่แล้ว +1

      @@ggeorge02 perfect score, easy dubs

  • @xsytrance
    @xsytrance 3 ปีที่แล้ว +1

    Thank you for this wonderful explanation with an equally wonderful accompanying visual!

  • @marsbunni_
    @marsbunni_ 4 ปีที่แล้ว +1

    Thank you sir, this is an excellent review! You're really saving me in college rn

  • @dndeveloper
    @dndeveloper 4 ปีที่แล้ว +1

    Best Explanation ever!

  • @Parmesanz
    @Parmesanz 3 ปีที่แล้ว +2

    Thank you a lot, Professor Dave!

  • @nikianderson2847
    @nikianderson2847 8 หลายเดือนก่อน

    I have been having trouble getting this. I think I actually do. Love the way you explain this

  •  5 ปีที่แล้ว +2

    Amazing explanation! Thank you

  • @shrinidhims5498
    @shrinidhims5498 5 ปีที่แล้ว +9

    3:57 whoohoo! You found volume of a sphere.

    • @krapsenhelb180
      @krapsenhelb180 4 ปีที่แล้ว +1

      Archimedes did it first 2000 years ago

  • @day35ofdebuggingthesamelin56
    @day35ofdebuggingthesamelin56 4 ปีที่แล้ว +3

    thank you, makes so much sense now

  • @abdeljalilpr2033
    @abdeljalilpr2033 6 ปีที่แล้ว +3

    Very nice and important and good way to present integral :)

  • @sleepydog9968
    @sleepydog9968 4 ปีที่แล้ว +2

    clear explanation. thanks for the help!

  • @ojaspatil2094
    @ojaspatil2094 3 ปีที่แล้ว

    genuinely so good, ty!

  • @arenabdwla5091
    @arenabdwla5091 3 ปีที่แล้ว

    Professor, best of the math

  • @janavjaiganesh7844
    @janavjaiganesh7844 2 หลายเดือนก่อน +1

    Dave U ARE THE GOAT

  • @dr.muhammadayyubkhan4523
    @dr.muhammadayyubkhan4523 3 ปีที่แล้ว

    Excellent Presentation. Regards and Love.

  • @choo1030
    @choo1030 4 ปีที่แล้ว

    I watched all your Calculus playlist and aced my Calculus final. And I didn't even read the class textbook!!!!

  • @idealmathsdeosir9308
    @idealmathsdeosir9308 3 ปีที่แล้ว +1

    Excellent Sir

  • @mathematicaa6876
    @mathematicaa6876 5 ปีที่แล้ว +2

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

  • @techteer8858
    @techteer8858 8 วันที่ผ่านมา

    it is a very good video and sir explained it nicely

  • @lunatickiller1494
    @lunatickiller1494 3 ปีที่แล้ว

    Im in love with that intro

  • @leenjundi3811
    @leenjundi3811 2 ปีที่แล้ว +1

    thankk uucramming this midterm n this helped

  • @iridium8562
    @iridium8562 4 ปีที่แล้ว +11

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

  • @gvhu3542
    @gvhu3542 5 ปีที่แล้ว +2

    Thank you very much...it was really helpful

  • @shibajeesarkar7846
    @shibajeesarkar7846 4 ปีที่แล้ว +1

    Thanks a lot. Very well explained. ❤️

  • @nanzzee22
    @nanzzee22 4 ปีที่แล้ว +1

    This helped me a lot...thankyou so much...😁👍