Arc Length (formula explained)

Arc length integral formula,

blackpenredpen,
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.

[megathetoxic]

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

[YourPhysicsSimulator]

Pythagoras is always here to solve our problems...

[tyronekim]

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

[garysnider]

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!!

[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!!

[weerman]

Love the intro. It's short and clear!

[DeerPrince]

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

[kylearby]

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

[NinjaMartin]

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

[ZhihanYang-io]

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

[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.

[jeanjulmis]

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.

[PhysicswithRoky]

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

[rob]

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) )?

[hikirj]

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

[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.

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.

[tsurutuneado]

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