Calculating Volume by Cylindrical Shells

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Professor Dave Explains

Professor Dave Explains

Күн бұрын

Пікірлер: 132
@simonlee7077
@simonlee7077 Жыл бұрын
Your 7 minute explanation with visuals helped me understand way more than the textbook's long text and the teacher's 1 hour lecture.
@danielolmos5315
@danielolmos5315 Жыл бұрын
CP SLO
@rayanallouzi8806
@rayanallouzi8806 3 жыл бұрын
I couldn't imagine what was happening for the life of me... this made it so clear, thanks a lot man.
@shreya8830
@shreya8830 2 жыл бұрын
This is probably the 3rd video that I am watching and I think all the animations that you use are very beneficial! Such videos are very helpful and they cover the basic of that topic in a very less time and that is highly appreciated!! Thanks!!
@bipedalnarwhal277
@bipedalnarwhal277 3 жыл бұрын
Way easier to understand than my textbook, thanks Professor Dave!
@AlexAlvarado-d2f
@AlexAlvarado-d2f Жыл бұрын
Professor Dave deserves every good thing that comes to him in life.
@audreyalvarez8576
@audreyalvarez8576 2 жыл бұрын
ive been lost for 2 semesters your video was the only one that made sense to me thank you for explaining it amazing
@codexcodexcodex
@codexcodexcodex 2 жыл бұрын
The animation in revolving the function is so satisfying.
@mryup6100
@mryup6100 4 жыл бұрын
Your explanations are otherworldly!
@Asad_Ullah
@Asad_Ullah 3 жыл бұрын
So you don't understand.
@oliehaku514
@oliehaku514 3 ай бұрын
man I'm studying for a test and I would've been absolutely screwed if not for your really easy to understand videos, thank you so much!
@mixalisp2867
@mixalisp2867 4 күн бұрын
lost the a two hour lecture yesterday that was about this video and the previous one with the disk. these 20 mins of video made up for the whole lecture. even the notes that i got from my classmates had the same examles! thanks Dave
@griest5493
@griest5493 3 жыл бұрын
I don't get how the average radius magically becomes r. Its clearly a value greater than r1 and less than r2 but you show it to be equal to r2 when you claim that 2*pi*r is the circumference of the outer circle at 4:07.
@yeetri1034
@yeetri1034 3 жыл бұрын
I was wondering the same thing
@brainloading5543
@brainloading5543 Жыл бұрын
I'd like to learn that kind of magic too
@lamaduchamatkapalihena9401
@lamaduchamatkapalihena9401 6 ай бұрын
they just make the difference so small that (r1-r2) which is delta r becomes dx in the limit, and when the difference is so small (r1+r2)/2 magically becomes r cus r1 almost equal to r2. dunno if this is correct.
@veronikabat8171
@veronikabat8171 6 жыл бұрын
I'm only in 8th form of school, i don't understand some things ,but i really like your videos. Thank you!
@38Fanda
@38Fanda 5 жыл бұрын
do it chronologically
@TheFirstNamelessOne
@TheFirstNamelessOne 5 жыл бұрын
Work hard, you'll eventually understand. I was in 7th grade when i was starting to wonder, why.
@crismal6477
@crismal6477 4 жыл бұрын
Nameless same I’m in 7th right now though
@colinking3314
@colinking3314 3 жыл бұрын
Im a senior and this shits rly hard lmao
@noahkatz263
@noahkatz263 Жыл бұрын
@@colinking3314lol and 7th grader really tryna understand it
@kiplangatenockmutai
@kiplangatenockmutai 3 жыл бұрын
Your work professor is marvellous I love it thank you so much, please add more work for calculating volumes,
@sukhmeetsinghsodhi3261
@sukhmeetsinghsodhi3261 2 жыл бұрын
The most to the point (time saving) and easy to understand teaching method. THANK YOU!!!!!!!!🙌🙌😍😍
@tiffingbird
@tiffingbird 2 жыл бұрын
Never thought i'd be coming to this channel for homework help and not watching you absolutely wreck the discovery institute but here we are i guess, thanks man
@RadoHudran
@RadoHudran 2 жыл бұрын
5:00 is the first time I heard we integrate from 0 to 2. Anyway, rn I don't get how Δr disappeared at 4:25, or how it became dx. I'll have to think that one through. In the future feel free to ask how, me if I'll find out I can explain
@TheeDeadCreator
@TheeDeadCreator 2 жыл бұрын
thats what im wondering...
@nezz0r
@nezz0r 11 ай бұрын
I think it is because: m = f'(x) = dy/dx = (f(x+a) - f(x)) / (x + h - x) = (f(x+a) - f(x)) / a so dx = a = x2 - x1 and in calculus as far as I know normally dx = Δx while dy != Δy. In this video r = x and by that dx = r2 - r1 which would be Δr. At least I think that is the reason why. If I'm wrong you may correct me.
@biggerthaninfinity7604
@biggerthaninfinity7604 3 жыл бұрын
Your video had great explanation, and I really liked that you had 3 dimensional models.
@Kiky_MedPhysicist
@Kiky_MedPhysicist 3 ай бұрын
Thank you sir for your dedication and for making this free! 🙏
@saurabhbabu284
@saurabhbabu284 5 жыл бұрын
U cleared my concept about volume using solid revolution. Thanku Sir
@christopher8199
@christopher8199 4 жыл бұрын
thank you professor Dave for making these videos
@tomasbeltran04050
@tomasbeltran04050 2 жыл бұрын
4:07 why does C have a circumference of a circle with the greater radius instead of the average radius? (In the graphic)
@Ando160794
@Ando160794 4 жыл бұрын
per my understanding 2pixh is a surface area of cillinder at point x and by integration through x basically we get area integrated through x and hence the volume of shape. That's how I see it.
@1em0n_ade
@1em0n_ade 8 ай бұрын
Surviving through your explanations this quarter 🙏 ... our professional did not care if the students understood
@selenaz6795
@selenaz6795 3 жыл бұрын
best video ever. I love you so much. U r literally saving the world by nurturing future scholars
@doomshroomish265
@doomshroomish265 4 жыл бұрын
professor dave saves my grade once again
@Velnio_Išpera
@Velnio_Išpera 10 күн бұрын
4:30 where is delta r in the integral?
@Velnio_Išpera
@Velnio_Išpera 10 күн бұрын
delta r is dx basically.
@AndrewRamirez-t9y
@AndrewRamirez-t9y 3 ай бұрын
This 7 minute video taught me more than a 2.5 hour lecture from my professor.
@jamessu-378
@jamessu-378 10 ай бұрын
Greatest professor in human history
@aliaaelborai9465
@aliaaelborai9465 7 ай бұрын
Thank you professor Dave for your great work.
@woodant1981
@woodant1981 2 жыл бұрын
Paying my uni 3k per year to watch KZbin on my own!! "Go to uni it'll be fun"😂
@user-lr2kp2dt5j
@user-lr2kp2dt5j Ай бұрын
Thank you, thank you thank you thank you so much. You are amazing. I didn’t know how to explain my feelings.
@szilike_10
@szilike_10 4 жыл бұрын
while findig the formula for the volume of the cilincrical shell, I don't get how could 2*pi*r be the circumference of the cilinder, since r2 is obviously the radius for its base circle, not the avarege radius. am I not noticing something?
@ProfessorDaveExplains
@ProfessorDaveExplains 4 жыл бұрын
the circumference of a circle is pi times its diameter, which is twice its radius.
@szilike_10
@szilike_10 4 жыл бұрын
@@ProfessorDaveExplains right but you said r was the average radius, not the bigger one
@szilike_10
@szilike_10 4 жыл бұрын
It might be though the difference is approaching to 0 when you deal with infinitessimals
@akbro23
@akbro23 4 жыл бұрын
@@szilike_10 still didn't get it. Did you understand?
@bisum1790
@bisum1790 3 жыл бұрын
Same doubt
@Attalla-t9b
@Attalla-t9b 7 ай бұрын
4:27 where does delta r go?
@Velnio_Išpera
@Velnio_Išpera 10 күн бұрын
delta r is dx basically.
@dummydummy5841
@dummydummy5841 Жыл бұрын
How will the formula change if the function revolved about a line other than y or x axis? Say it revolved about x=4.
@chinmayeeshabadi5349
@chinmayeeshabadi5349 4 жыл бұрын
Nicely explained the main concept.
@thegrandweasel1926
@thegrandweasel1926 4 ай бұрын
why is it when calculating volume of a revolution with circles, we integrate a circle without a thichness onlly pi*r^2 but with cylindrical shells we add a thickness, why can't we use 2pi*r*h?
@thegrandweasel1926
@thegrandweasel1926 4 ай бұрын
I just realised the thickness (delta r) may just be dx but I am not sure
@rickychaos7119
@rickychaos7119 3 жыл бұрын
ty for helping me more than my college professors
@babakshahed
@babakshahed 5 жыл бұрын
perfect, thank you so much
@neonknowledgehub9172
@neonknowledgehub9172 3 жыл бұрын
In comprehension , why you put integrated version of the f(x) in V formula . Please explain 1nd and 2nd step
@laibaashfaq4535
@laibaashfaq4535 5 жыл бұрын
suppose that a cylindrical can is designed to have a radius of 1 inc . and a height of 5 inc, but that the radius and height are off by amounts dr=+0.03 and dh=-0.01. estimate the resulting absolute change in the volume of a can
@qazimuhammadosama7381
@qazimuhammadosama7381 3 жыл бұрын
How the equation was written at 4:25 ?
@thisriceiswhite5371
@thisriceiswhite5371 Жыл бұрын
THE ABSOLUTE BEST
@Algebrainiac
@Algebrainiac 11 ай бұрын
Is this not on a calculus textbook??? I can’t find it anywhere. Maybe I’m looking wrong
@siphamandladhlamini8688
@siphamandladhlamini8688 5 жыл бұрын
Professor Dave you are the best.
@bbugrayuksel
@bbugrayuksel 2 жыл бұрын
I understand that we just call the average value of the radii 'r', but why did we call (r2-r1) delta r? I did not get that part at all.
@alvideor
@alvideor 2 жыл бұрын
r2 - r1 is how much we have moved along the x-axis to get the next cylindrical shell, so this is delta x. When we integrate, we make each shell infinitely thin and so we set this delta x to approach 0 in the limit. You can think of this approach as those old style pirate telescopes that have smaller cylinders inside larger cylinders and can extend or collapse. Only here you've got infinitely many of them and each one is infinitely thin. The height of the cylinders follows the function. When you collapse them all inside each other, you get the whole bundt cake. When you integrate you're summing up the infinitesimal volumes of the cylinders by going along the x-axis (moving r2-r1 by an infestimal amount each time). You only need to integrate from 0 to 2 because each change in x gives you the whole cylinder shell. no need to worry about -2 to 0, that volume is already included.
@TheAuraEngineer
@TheAuraEngineer 4 ай бұрын
Why are we able to swap out the average of r for r?
@dexiexo2199
@dexiexo2199 2 жыл бұрын
Can I integrate the surface area of a cylinder without the top and bottom area to get the solution
@doumasama5654
@doumasama5654 5 жыл бұрын
Very good explanation
@studiant3004
@studiant3004 3 жыл бұрын
Thanks Jesus, I knew you would help me some day!
@jean-pierrevandermerwe7604
@jean-pierrevandermerwe7604 4 ай бұрын
This bundt cake looking thing cracked me up lol
@ddroidgaming13
@ddroidgaming13 9 ай бұрын
Im so amazed I actually got it correct thank you
@alialawadhi8096
@alialawadhi8096 5 жыл бұрын
How did u get the 0 to 2 interval?
@pchander100
@pchander100 5 жыл бұрын
Because we are trying to find the volume generated by rotating the curve between x=0 and x=2.
@aimanaltaf8872
@aimanaltaf8872 2 жыл бұрын
Can please u expalin how can we take value of a and b if it is not mention in question
@epicm999
@epicm999 Жыл бұрын
You find the zeros of the function. Set the function equal to 0 and solve for all values of x, then look for the two positive values and see if they fall within the bound you're given. Hope this helps!
@sainathreddyvarikuti4835
@sainathreddyvarikuti4835 6 жыл бұрын
Why u took mean radius 'r' in total volume
@alvideor
@alvideor 2 жыл бұрын
At the limit we set Delta r to equal 0, and so r2-r1=0. At that point r2=r1=r and r2 + r1 just equals 2r. No need to bring up the average even, just keep in mind that at the limit we're dealing with infinitesimals.
@Lalalalalalaallala
@Lalalalalalaallala 4 жыл бұрын
Can anyone explain how he got the range 0 to 2
@MakeupByAnanyaSharma
@MakeupByAnanyaSharma 4 жыл бұрын
Because it is when the function crosses x-axis again You can see in the beginning he took only a certain region to "wrap" around the y axis and that region varied from x=0 to x=2. { equate f(x) to zero and we get two roots ..0 and 2 }
@tauntaun71
@tauntaun71 3 жыл бұрын
@@MakeupByAnanyaSharma Thank you!
@CECELIAOWUOR
@CECELIAOWUOR Жыл бұрын
How did you get the radius please
@tdrawdy2
@tdrawdy2 2 жыл бұрын
Where did you get the limits of integration in the main example shown?
@dramaticreaper
@dramaticreaper Жыл бұрын
Same thought, I think he forgot to mention that it was a made up example.
@angelineconsulta6723
@angelineconsulta6723 5 жыл бұрын
Is the solution still the same even if there is another given like y=1. Does it matter in solving this.
@krapsenhelb180
@krapsenhelb180 4 жыл бұрын
I guess it's only the border of the integration
@anysianas5099
@anysianas5099 4 жыл бұрын
Thank you professor Dave
@anuragtiwari2270
@anuragtiwari2270 6 жыл бұрын
Sir plz also make a tutorial about physics or astronomy.. waiting for it. From the last 1 year. Only math series is going on
@ProfessorDaveExplains
@ProfessorDaveExplains 6 жыл бұрын
buddy, i've done like 60 tutorials on physics already! astronomy is coming very soon, i'm filming it now.
@pchander100
@pchander100 5 жыл бұрын
Brilliant..!
@az4475
@az4475 4 жыл бұрын
Where is the thickness in the volume formula when you integrated it?
@xxmemestar69xx82
@xxmemestar69xx82 3 жыл бұрын
It’s just dx.
@ya00278
@ya00278 5 жыл бұрын
you deserve more subscribers!
@infernalspy0176
@infernalspy0176 4 жыл бұрын
Ikr I was thinking the same
@md.sirazulislam883
@md.sirazulislam883 5 жыл бұрын
thanks mr
@atulbarman7750
@atulbarman7750 2 жыл бұрын
Thank you sir
@purpetualbeats
@purpetualbeats 4 жыл бұрын
Dave is the goat
@aiqnvc8883
@aiqnvc8883 3 жыл бұрын
thanks for the video
@bl5550
@bl5550 Жыл бұрын
Why did you evaluate from 0 to 2
@tristanchisholm5857
@tristanchisholm5857 4 жыл бұрын
Thank you so much
@beratdikmen6117
@beratdikmen6117 6 жыл бұрын
it is very useful thx
@JJmyri
@JJmyri 8 ай бұрын
isnt it wrong in 4min mark, the line C should be in between r2 and r1
@Rahoz-mg6gw
@Rahoz-mg6gw 3 жыл бұрын
U are the best and i hope u know that .
@kellyli9561
@kellyli9561 4 жыл бұрын
why make a value from 0 to 2 how did it come
@samialjailani5587
@samialjailani5587 3 жыл бұрын
solve for y=0 and find the x intercepts
@be.on_teach7415
@be.on_teach7415 3 жыл бұрын
Thank you
@slickyy21
@slickyy21 Жыл бұрын
Tried Solving the comprehension check Problem- Wasted more than 2 hours, but couldn't really solve after all-i understand the concept but i just got stuck at arithmetic shit at the end- These kind of things really mess with your motivation....... Should i give up?
@silkynarula1556
@silkynarula1556 4 жыл бұрын
Why didn't dy in place of dx?
@hana29971
@hana29971 2 жыл бұрын
Because we used the technique of cylindrical shells we don't have to make things in terms of y
@sheababeyeah
@sheababeyeah 5 жыл бұрын
best explanation on this topic, goooood shit
@SoGodCreatedManInHisOwnImage
@SoGodCreatedManInHisOwnImage Жыл бұрын
thank you, Mathematixcs Jesus
@sts2485
@sts2485 7 ай бұрын
How tf did r1+r2/2=r???
@thuclinhoannguyen3334
@thuclinhoannguyen3334 11 ай бұрын
thank you professsorrrrrrrrrrrrrrrrr
@jester60ify
@jester60ify 2 жыл бұрын
I thought that you were dealing with a cones shaped curve
@pranjalchand6792
@pranjalchand6792 8 ай бұрын
@justinbrannon6391
@justinbrannon6391 2 жыл бұрын
uhhhh are the bounds the x intercepts or y intercepts
@themysteriousfox3767
@themysteriousfox3767 2 жыл бұрын
thanks math jesus
@eudaimoniapeisithanatos2252
@eudaimoniapeisithanatos2252 4 жыл бұрын
00:09 here you go
@refus_global
@refus_global 2 жыл бұрын
soo.. the volume of big jello
@aheedatif6326
@aheedatif6326 Жыл бұрын
Istg old professors needs to retire if they can't help their students 😒
@anjanaa5715
@anjanaa5715 Жыл бұрын
Hlo
@zoya808
@zoya808 3 жыл бұрын
h
@marvinclark7277
@marvinclark7277 Жыл бұрын
why you add +1 on the "2x³- x⁴" that it has been already a power rule?
@sundeepuppal965
@sundeepuppal965 2 жыл бұрын
Thank you!
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