Area of Surfaces of Revolution | Derivation & Example

Рет қаралды 70,529

5 жыл бұрын

If we revolve a curve around an axis it forms a surface. We can use Calculus to compute the area of this surface, much as in Calculus I we computed the volume contained in this region. The derivation of this formula works in much the same way.
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Пікірлер: 88

@funwithwaniarumaisaareeba7586 4 жыл бұрын

No one in the whole KZfaq has explained this concept as much clear as you did. Hats off to you. Really deserve much more views.

@firsttnamee3883 4 жыл бұрын

yes

@kimberlyann1022 3 жыл бұрын

I cannot agree more with this. I watched all of his ads as my thank you

@arnavbhavsar8567 4 жыл бұрын

This guy is definitely the best teacher on youtube.

@deyomash 3 жыл бұрын

So, funny, but. I'm a graduate theoretical physicist but until now i have not understoof why in the AREA you need to take the arclength but in the volume you're okay using just "dx" (just pi * f(x) ^2 dx) even though the little cylinders are still "curved"..

@DrTrefor 3 жыл бұрын

this happens so often that a little thing from calculus or whatever is missed, happened to me all the time in grad school, like how did I not know this?

@deyomash 3 жыл бұрын

@@DrTrefor no you dont understand, i literally dont know still. Pls tell me hahaha

@moazamkhan 8 ай бұрын

Yes WTF

@stephaniegarcia8557 4 жыл бұрын

Just found your channel and all I can say is WOW. I love the way you teach! It's very clear and easy to follow along. Definitely subscribing!

@firsttnamee3883 4 жыл бұрын

the most underrated math channel in youtube

@angelfernandez4235 5 жыл бұрын

Really great explanation & illustration! Had so much problem imagining it but the way u visualised it rly help,thanks a lot!

@leadersheir9377 4 жыл бұрын

"So in place of the width, I'm gonna come along here and put in that square root of *all that nonsense*" 🤣🤣🤣 Absolutely LOVE your content, professor!

@js7244 3 жыл бұрын

Thanks Trefor!! once again you are saving me so much time and giving me real insight in to the subject

@felipeseixas7028 8 ай бұрын

We are watching a master at work 😎

@SpazzHobo 2 жыл бұрын

The visual made it very helpful for me. The trick is to relate the surface area here to the idea of how the surface area of a cylinder is derived from a rectangle. That idea combined with your visual made it clear for me. Thanks!

@Areyouserious1 3 жыл бұрын

my doubt is why dont we use the arc length formula when finding the volume generated by the revolving function....There we only take the width as dx

@madhavanand756 4 жыл бұрын

It's beautiful the way you have explained, directly goes in my head. And it is totally unique the way you explained

@adnanmohamed6517 4 жыл бұрын

8:28 minutes is way more better than 1 h lecture. ( I don't know who said to these professors that math is just solving examples using formulas that you don't know from which hell they came from) Thanks alot

@zihuiwang8649 4 жыл бұрын

Thank you! Really helped my maths project at school!

@nazihnassar2101 4 жыл бұрын

the best video on the internet explaining this topic p.s you saved my life

@eyadnasir6802 Жыл бұрын

Amazing! Thank you for a unique way of explaining this.

@aslpelinsuozturk3106 5 жыл бұрын

You deserve a lot more views. This is an amazing video.

@subhradeepghosh2523 Жыл бұрын

I was struggling with the derivation. This video helped me a lot. Thank you.

@alisapuskala1437 2 жыл бұрын

Super clear explanation, and an intuitive explanation. Good material for an ia

@royalzak4019 5 жыл бұрын

Your teaching style is awesome Love from India.

@renefsierra 2 жыл бұрын

Thanks, great explanation

@ananyaprakash4262 4 жыл бұрын

Your videos are so well done🤗

@hmudisalam 3 жыл бұрын

excellent !!

@lukaskamin755 5 ай бұрын

Cool explanation. Thumbs up 😀

@cesarreategui2693 3 жыл бұрын

THIS GUY IS THE BEST!!!!!!

@IlIlllIlll Жыл бұрын

That really helped, thx🙏🙏

@peon3715 3 жыл бұрын

Just amazing. I subscribed inmediatly, I don´t know why he doesn´t have more subscribers.

@DrTrefor 3 жыл бұрын

Haha right!?

@albertmendoza1468 4 жыл бұрын

Understandable. Have a nice day!

@iknowimreal 3 жыл бұрын

Thank you

@DrTrefor 3 жыл бұрын

Glad it helped!

@treasuresoffaith7027 2 жыл бұрын

I really like your videos. 👍

@tiagoantonio2343 2 жыл бұрын

fantastic

@kin_1997 2 жыл бұрын

thank you for this :)

@fernandotanase114 Жыл бұрын

Could you also link the mentioned videos in the description box, please. It'll make it easier for students that have multiple browser tabs open and trying to understand the concepts while watching the videos.

@Pranav_prince 3 жыл бұрын

Superb explanation and understood well in single watch

@DrTrefor 3 жыл бұрын

Glad it was helpful!

@davidhofmann4857 2 жыл бұрын

You are an awesome teacher, thanks!

@DrTrefor 2 жыл бұрын

Glad you think so!

@prateeksingh974 4 жыл бұрын

Too good

@shreeramshreyas9761 3 жыл бұрын

U d best man !!! I have a small doubt Tho. Why can't we consider the ribbon as an cylinder instead of a circle ?

@siddharthkhandelwal933 Жыл бұрын

Thanks!

@DrTrefor Жыл бұрын

Thank you so much, you're amazing!

@anaidamadhavan1271 3 жыл бұрын

You are the best man. I understood this so much clearly. Thanks alot🤗🤗

@DrTrefor 3 жыл бұрын

Happy to help!

@anaidamadhavan1271 3 жыл бұрын

@@DrTrefor subscribed 😊

@nicholasbolte2248 2 жыл бұрын

enjoyed the video, was just wondering what software you use to show the 3D model (including the z axis)

@willthecat3861 Жыл бұрын

It was all good... particularly the invocation of the 'mean value theorem ' to justify using the derivative... it was all good until the end when he didn't point out that... except for some trivial families of 2-D curves... the integrals can be very difficult to evaluate non-numerically. Profs always choose an example your cat can calculate, and then leave you to burn your brain trying to do ones that require a bag of obscure integral tricks.

@fan-gq8lj 6 ай бұрын

life saver

@gaureshnaik7248 3 жыл бұрын

Sir u teach so well 😊😊

@DrTrefor 3 жыл бұрын

Thank you!

@ashishKjr 4 жыл бұрын

Initially you say x_i * is some point in the partition (and I assume by some, you mean arbitrary) but later it seems like x_i * depends upon ∆y_i and ∆x_i by mean value theorem. So, doesn't x_i* depends upon the partition and is not arbitrary?

@rayenwiller 3 күн бұрын

really wanna know how to make those animations and graphs, using what software

@mellifluousb.4549 Жыл бұрын

Doesn't the formula need an absolute value for f(x)? I mean if the curve we examine is f(x) = -x^3 with 0

@toomanycharacter Жыл бұрын

2:51 We're not going to worry about the difference between the bigger and smaller radii, because in the limit it's going to be smaller and smaller 3:43 But we ARE going to worry about the difference between the "Width?" and dx, despite the fact that in the limit it's going to be smaller and smaller? Why the distinction? I mean, if we would decide not to worry about both of those small differences, then we would get 2pi * f(x) * dx as the surface area. If we decide to worry about both of those small differences, then I don't even know how we would get any surface area at all. Clearly, the distinction is very important, but why did we decide to make it?

@toomanycharacter Жыл бұрын

I think I kinda get it now. The absolute difference between the radii is going to be smaller and smaller, and the relative difference between them is going to be closer and closer to 1. So in the limit, the two radii will be equal in both ways. The absolute difference between the "Width?" and dx is going to be smaller and smaller, but the relative difference between them is not going to be closer and closer to 1 - it's going to be closer and closer to sqrt(1 + (f'(x))^2). So in the limit, as dx and "Width?" approach zero, "Width?" is going to be a constant multiple of dx, so the widths will not be equal in both ways. Because the radii are equal in both ways, we can think of the surface area as the surface area of a cylinder, with the "Width?" being the cylinders width. In a strange way, in the limit, "Width?" becomes parallel to the x-axis while remaining a constant multiple of dx. Is my interpretation alright?

@dudeiknowman Жыл бұрын

@@toomanycharacter i had the exact same question as the original comment, and your interpretation feels insightful. In that strange way, in the limit, the width is parallel to the x axis, but remains some constant multiple of dx. Wish we could get professor Bazett's thoughts on it.

@rfc7643 3 жыл бұрын

why we can't find area of surface only by circumferences without width?

@BilalAhmed-on4kd 5 ай бұрын

why don't we think of it as finding the sum of the curved surface areas of infinitely many cylinders, since the width is infinitesimally small, it's curvature should not matter, just like in volume

@mnada72 3 жыл бұрын

0:50 Do you have a video on this topic in the Calculus I playlist?

@DrTrefor 3 жыл бұрын

This is part of the Calculus II playlist as I have it, but each college or university does it a tad differently.

@mnada72 3 жыл бұрын

@@DrTrefor Thank you, what I mean is the calculation of a volume enclosed by a curve I couldn't find a video on either calculus I or II in the playlist .

@user-uh8wk5uy9n 2 жыл бұрын

Find the surface area due to the rotation of the area between f(x)=x^3 and g(x)=x

@dvsalim09 2 жыл бұрын

Hello Dr. Trefor, I really find your videos helpful. Just need to know, how can I cite your videos?

@DrTrefor 2 жыл бұрын

A link is fine!

@dvsalim09 2 жыл бұрын

@@DrTrefor Thank you

@ezequielsm Жыл бұрын

thankyouthankyouthankyouthankyou

@MrMarkgyuro 4 жыл бұрын

dear Trefor why we divide 2phi by 36 in the last part?

@MrMarkgyuro 4 жыл бұрын

@@DrTrefor so we solve for 1/36. Like 1/36 * du/dx = x^3? im lost :)

@MrMarkgyuro 4 жыл бұрын

@@DrTrefor no i see sorry :D du/36 = x^3 dx..

@thezoz9476 3 жыл бұрын

Why isnt the width dx

@zechang573 2 жыл бұрын

😊

@zechang573 2 жыл бұрын

thanks for teaching

@user-fn7vs6pb6n 9 ай бұрын

For those looking for Arclength Formula video, here you go kzfaq.info/get/bejne/pq5dgtCbksmxn58.html.

@suleymanemirakin 2 жыл бұрын

still dont understand why we dont take delta x

@luisramos3748 4 жыл бұрын

circunference....

@amaljeevk3950 Жыл бұрын

🥰

@jansmith7387 2 жыл бұрын

Why is my answer negative?

@logical29 2 жыл бұрын

You talk like Krieger from ArcherFX

@natty1 2 жыл бұрын

no idea what just happened im just dumb

@marklourencelucas9495 4 жыл бұрын

Goodbye organic chemistry

@Linhkinhbrods 13 күн бұрын

why u try to teach like a smartarse

@maxjang2446 Жыл бұрын

hey man, thank you for saving my ass for a math investigation paper🫶