Arc Length (formula explained)

Arc length integral formula,
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math for fun

[@blackpenredpen]

Minor picky mistake, *Please write "dL" instead of "dl".* Because when we integrate dL we will get L. While integral of dl is l.

[@sairampatnaik1]

Ok sir

[@sairampatnaik1]

@Tigc channel 2 why

[@wikingandersson2561]

I have a question: Would it be possible for you to derive (show how on heavens earth) the formula of: Int sqrt (a^2-x^2) dx = x/2(sqrt a^2-y^2) - a^2/2(sin^(-1)(x/a))+c Hope I got it right. Found it in a table for a probkem I have but I am sooo lost in the integrationworld. Would be nice to see different derivations with some simple graphics on the board as well. Thank you sir, for your work, it is appriciated all over the world!

[@luddelagerstedt6458]

dl also means decilitre :)

[@sophiacristina]

What an amateur... Unsubbed >:(

[@megathetoxic]

2:07 "And now, here is the dL.."

[@kapishjalan7393]

Ahahaha

[@YourPhysicsSimulator]

Pythagoras is always here to solve our problems...

[@keshavchaturvedi4015]

Budhayana*

[@fifiwoof1969]

Better that than Gougu!

[@maxwellsequation4887]

Thank you papa Pythagoras 🎉💐

[@ahduiiiiiiiii]

@@fifiwoof1969 bro it’s the same

[@tyronekim3506]

Very good explanation. I'm in disbelief that some people don't like it.

[@lunam7249]

Pathagorean’s!!! They don’t like anyone!!!

[@faisalmohamed4595]

Maybe because there were no questions on the vid?! But the video is still great tho

[@veilofmayaa]

I can't tell you how happy I am to have come across your channel. Nobody has explained this concept as clearly as you have. It is so important to understand what the formula stands for and this is right on the money! Thank you so much!!

[@weerman44]

Love the intro. It's short and clear!

[@blackpenredpen]

weerman44 thanks!!!!! It was done by Quahntasy!

[@MarioPlinplin]

I was about to say LITERALLY the same lol

[@weerman44]

@@MarioPlinplin Lol nice :D

[@garysnider5342]

It takes 7 seconds to skim the proof from the textbook. It took 7 minutes to understand the proof in this video. Absolutely worth it. Amazing job and thank you!!

[@tsurutuneado5981]

I was searching for a video like this some weeks ago, so happy you uploaded it, thank you

[@DeerPrince]

It's amazing that you explained in 6 minutes what my calculus teacher couldn't clearly explain in 1 hour.

[@AnjaliSharma06]

Amazing teachers like you make me love maths even more , thank you

[@ZelForShort]

Perfect timing. Self teaching my self line integration and this is a great explanation for part of that crazy formula int(f(x(t), y(t))√((dx/dt)^2 + (Dy/dt)^2) dt

[@kylearby2988]

You’ve helped me so much with my calculus class, you explain all of these complex subjects so well. Thank you!! I’ve subscribed!

[@evelinageorge2997]

Sure👍

[@gloystar]

Very nice video bro. I remember I did the exact same derivation when I was studying calculus, but then realized this derivation is in fact incomplete, because the pits of (dy) are not necessarily equal in length, but the pits of (dx) are, and I saw text books use the mean value theorem in their derivations to overcome that.

[@hikirj]

I absolutely love your videos man. You are the best math KZbinr I know and recommend you to anyone I can.

[@NinjaMartin]

So incredibly clear! Thank you so much for creating these fantastic videos ❤

[@blackpenredpen]

Glad you like them!

[@user-tg7bv1rk3k]

Bro your video is so funny I kept smiling watching it - while learning a lot! Thanks!

[@jeanjulmis2347]

That was very clear and concise. The textbook sometimes gets very confusing. Now, I can go back and read the textbook again on this chapter.

[@MrPeradjokic]

Good explanation and straight to the point. Thank you for the video!

[@Kevin-cy2dr]

You sir, deserve a medal. Great explanation 👍👌

[@gordongorgy9148]

That intro is perfect

[@blackpenredpen]

Thanks.

[@calistairene998]

loves the explanation, short and clear

[@aidanowens8766]

You're awesome! I appreciate your enthusiasm!

[@CPTsack]

You explain this perfectly. Thank you!

[@PhysicswithRoky]

Now, I can solve any problem regrading this. You made the basics. Thank you.

[@ButterDJar]

thank you so much, i saved so much time by understanding in just 5 minutes instead of reading a 5 page long of contents inside my textbook.

[@ece_47_debajitpaul9]

Perfect explanation

[@adarbarandalgic2730]

Great explanation.

[@light-qn2jb]

fantastic explanation

[@Bodyknock]

Seems like a natural followup would be when the curve L is a function over time t from time a to time b (e.g. F(t) = (sin(t), cos(t)) in the cartesian coordinates to describe a circular path) and looking at the integral over dt.

[@Randomguy-vl6gi]

Nice work

[@sardarmuhammad9254]

thank you for making this video .

[@RSA_Shock]

God I love your enthusiasm

[@zubmit700]

Could be fun with some arc battles. Also thank you for your videos.

[@biswaruppramanik2007]

Wow, you are doing a great a job by making us understand complex topics like these.🙂

[@emontrailers]

very good explanations

[@hyojupark4360]

Thank you so much!! you're a hero 💗💗💗💗👍

[@Towl35]

This is the simplest way I've seen it explained!

[@chyawanprash]

Wow, this is amazing!

[@SempatikBalkc]

best teacher ever

[@ajeetkumar5453]

Thanks a lot bro for your help.

[@dimbanimvula3672]

Thanks a lot

[@witsey6345]

Best teacher You helped me a lot thank you!

[@stevengaleano7759]

You just saved me bro. I love you!

[@oneworldT1]

Thanks sir .

[@hoodiedude4204]

Haha I worked out the same formula when I did this for fun once. Showed it to my professor and he showed it to the whole class.

[@RiteshNEVERUNIFORM]

Your videos are addictive

[@user-rc7cb3oq3u]

thank you so much sir ❤❤

[@mrman5066]

Holy, this guy is brilliant! I've seen him once before but only at a glance. So glad I found this video, you don't need to tell me twice to subscribe.

[@MisterTomahawk22]

Really nice formula !

[@omarraafat1228]

U'r so simple i liked that soo much❤️❤️❤️

[@sangamxghimire]

thank you very much

[@awwab1094]

I appreciate it thank you

[@6612770]

Excellent that you identified how the 'elemental length' is constructed in terms of the coordinate space. Getting this firmly grasped is key to tackling the 'bigger stuff' - circle, ellipse, spirals - then onto 3D with helix et al. Please use this episode as a launching point for a series, working upwards through the understanding/complexity of finding arc lengths 'from first principles'. That is what will make the "Aha!" Light Bulb come on in peoples heads and stay there forever.

[@AbhishekSachans]

Exactly!!

[@UntakenNick]

Yeah, I wish there were channels that teach math of physics at full depth starting from zero instead of just making use of that knowledge to do random stuff that require the view to already know the subject in order to understand what they're talking about.

[@CyberGamer1539]

This is easily the simplest way I've seen of deriving the formula.

[@serjanholder2053]

Thank you! Such a clear explanation! Also, the ball in your hand reminds me of the Ood, an alien species of the sci-fi show dr. Who.

[@abhiramijayan1716]

Thank you so much..much effective 👍 and very clear

[@AnuragKumar-io2sb]

Wow😲😲 never thought of this

[@johnny_eth]

It would be cool for you to demonstrate the arc length formula with a practical example, like the arc length of the semi circle (x**2+y**2=r**2) and then resolving to pi.

[@evelinageorge2997]

Sir you know the importance of understanding 👍❤️

[@rob876]

Thanks for this. Your explanations are brilliant. There's another case when x and y are parameterised. e.g. if you have the circle defined by x(s) = r.cos(s), y(s) = r.sin(s) and you want the arc length between s = 0 and s = 2π dl^2 = dx^2 + dy^2 dx = dx/ds ds = -r.cos(s) ds dy = dy/ds ds = r.sin(s) ds so dl^2 = r^2 (cos^2(s) + sin^2(s)) ds^2 dl = rds L = r∫[0 to 2π] ds = 2πr Please could you show us how to calculate the arc length of an ellipse? ( x(s) = a.cos(s), y(s) = b.sin(s) )?

[@professorpoke]

To find the complete arc length of an ellipse find the quarter arc length (using all positive values), and then multiply it by 4.

[@m.f.3347]

Lowkey flexing with the supreme 👀👀

[@alicia4940]

Thank you so muchhhh😍😭 you‘re much better than my uni lecturer😍

[@Ken-no5ip]

Amazingly simple

[@MrMariuslestat]

Thank you!!!!

[@Amine-gz7gq]

You rock man !

[@rohitsk4018]

Very very good Thank you sir

[@xobieu]

for anyone's confused at 3:54 why (dx)^2 + (dy)^2 = (dx)^2 * ( 1 + (dy)^2/(dx)^2) ) since (dy)^2 = (dy)^2 . (dx)^2 / (dx)^2 (which is = 1) u can basically create a dx out of thin air. Then, obviously, we just need to factor the dx out (dx)^2 + (dy)^2 * (dx)^2 / (dx)^2 = (dx)^2 * ( 1 + (dy)^2/(dx)^2)

[@DanielFrostable]

Thank you! My book was not clear in how this formula came about.

[@vakhariyajay2224]

Thank you very much. 👍👍🔝🔝

[@dharmanshah1239]

Nice intro!!

[@juancuneo8346]

Amazing

[@popodood]

After relearnijg little segments of math randomly it seems so simple each time lol, but it is hard to remember how to derive all these in the moment

[@holyshit922]

there are more cases fe curve given by parametric equations curve in polar coordinates

[@avery_IO]

dope shirt @blackpenredpen

[@bazzkiller1331]

Great video, well done! If I were you, I wouldn't use dx and dy at start, but *Δx* and *Δy* as they are not infinitesimal.

[@JensenPlaysMC]

well obviously he is assuming they are. just blown up for viewing purposes.

[@rafaellisboa8493]

wooow this was awesome mind blown comrade

[@carcisme]

Medio entiendo el inglés, pero se entiende perfectamente lo que explicas. Gracias.

[@garyhuntress6871]

I've done line integrals before but now I know WHY they look like that!!

[@RicardoOliveiraRGB]

Will you talk about line integrals?

[@chathurangasameera6722]

Tnx sir ❤️

[@bulldawg4498]

Will you ever make videos covering line integrals over scalar and vector fields, culminating in Green's Theorem and Stokes' Theorem? Also, smaller in scope: there's a need for a good video on the Jacobian ...

[@rafaellisboa8493]

please could you do a vid about the area of a 3D curve? that should be very interesting

[@kono152]

could you make a video deriving the arc length for polar curves too?

[@anilkumarsharma8901]

show time dilation between two points as direct length and curve length of various type like parabola or circle or any other geometric figures

[@nfqioehr]

Hi, do you have a video on how to graph a cycloid and an epicycloid given a their parametric equations? thanks a lot !

[@gabrielzago387]

Nice!

[@arnabchowdhury4892]

Please derive surface area of cone, cylinder, sphere using surface integral around axis of rotation

[@DeLuini985]

Thank you so much. You reminded me of using Pythagoras everywhere 🤣

[@professorpoke]

Gogou theorem

[@GrouchierThanThou]

I would have expected this video to include parameterized curves as well... As you might have for curves where y isn't a function of x nor x of y.

[@kohi_kohi]

Love the Doraemon theme in the background

[@husklyman]

I wanna challenge you to find a way to calculate the integral that gave π(at least 2 digits) without calculators!!! And remember, before π discovered, you couldn't use it because...

[@user-ov6ee1nk9o]

Here is the "dL" lmao, great video!

[@astaghfirullahalzimastaghf3648]

Hi.. Thank you for this information.. Now i ask myself is this formula valid to be used for a circle function or oval function.. Because the initial point of x that im concern might be bigger in terms of value than the destination of point x. Assuming, that i am trying to calculate the distance between these two, do i need to insert the initial point or the destination point first in the arc formula L=integrate √(1+(f'(x)^2) dx ?

[@mihajlovucic8037]

Hi, Blackpenredpen. I like your videos and I learned a lot about calculus in your videos (although I'm 15, and we don't do it in school yet :)) I am interested in limits, so I found this one: lim (n-->inf) 4/n*(sqrt(2/n-1/n^2)+sqrt(4/n-4/n^2)+sqrt(6/n-9/n^2)+sqrt(8/n-16/n^2)....+sqrt(2k/n-k^2/n^2)...). Can you compute it? (You can put it in sigma calculator to see how interesting it is)

[@lunam7249]

Excellent work young man!!

[@maxhaibara8828]

Say "ruler" 10 times in a row

[@anilsharma-ev2my]

Can you found the equal area circle ? Radius is what so we found percentage of curve length between interval ?

[@SumitSharma-wf5xb]

Please integrate it [sqrt(cos2x)]/sinx

[@algirdasltu1389]

Its always pythagoras that shows up everywhere, even when you dont expect it...

[@h4c_18]

And if you have x(t) and y(t) you do the integral sqrt((dx/dt)^2+(dy/dt)^2)dt from t_a to t_b? Ex: x(t)=e^t * cos(t) and y(t)=e^t * sin(t) from 0 to Pi/2

[@shotto9167]

I cannot believe I thought the same thing, but I didn't do everything just because I don't know calculus yet. Actually, I did a formula for the linear functions, however I wish I could do a generalization of that.