Arc Length (formula explained)
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- čas přidán 26. 10. 2018
- Arc length integral formula,
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blackpenredpen,
math for fun
Minor picky mistake,
*Please write "dL" instead of "dl".*
Because when we integrate dL we will get L.
While integral of dl is l.
Ok sir
@Tigc channel 2 why
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!
dl also means decilitre :)
What an amateur... Unsubbed >:(
2:07 "And now, here is the dL.."
Ahahaha
Pythagoras is always here to solve our problems...
Budhayana*
Better that than Gougu!
Thank you papa Pythagoras 🎉💐
@@fifiwoof1969 bro it’s the same
Very good explanation. I'm in disbelief that some people don't like it.
Pathagorean’s!!! They don’t like anyone!!!
Maybe because there were no questions on the vid?!
But the video is still great tho
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!!
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!!
New intro by Quahntasy! He is awesome and creative! Check him out czcams.com/channels/tlaa8gywhvUdrcdYQf5QQQ.html
Thanks again :)
Very clear and concise video, good work!
I was searching for a video like this some weeks ago, so happy you uploaded it, thank you
You’ve helped me so much with my calculus class, you explain all of these complex subjects so well. Thank you!! I’ve subscribed!
Sure👍
It's amazing that you explained in 6 minutes what my calculus teacher couldn't clearly explain in 1 hour.
Love the intro. It's short and clear!
weerman44 thanks!!!!! It was done by Quahntasy!
I was about to say LITERALLY the same lol
@@MarioPlinplin Lol nice :D
So incredibly clear! Thank you so much for creating these fantastic videos ❤
Glad you like them!
I absolutely love your videos man. You are the best math CZcamsr I know and recommend you to anyone I can.
Amazing teachers like you make me love maths even more , thank you
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.
That intro is perfect
Thanks.
Bro your video is so funny I kept smiling watching it - while learning a lot! Thanks!
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
Good explanation and straight to the point. Thank you for the video!
You sir, deserve a medal. Great explanation 👍👌
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.
You're awesome! I appreciate your enthusiasm!
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.
You explain this perfectly. Thank you!
loves the explanation, short and clear
Could be fun with some arc battles.
Also thank you for your videos.
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.
Wow, you are doing a great a job by making us understand complex topics like these.🙂
Now, I can solve any problem regrading this. You made the basics. Thank you.
thank you for making this video .
Nice work
fantastic explanation
Great explanation.
Lowkey flexing with the supreme 👀👀
Thank you so much!! you're a hero 💗💗💗💗👍
Perfect explanation
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.
Wow, this is amazing!
God I love your enthusiasm
U'r so simple i liked that soo much❤️❤️❤️
This is the simplest way I've seen it explained!
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.
You just saved me bro. I love you!
very good explanations
Best teacher
You helped me a lot thank you!
Thank you so much..much effective 👍 and very clear
Thank you so muchhhh😍😭 you‘re much better than my uni lecturer😍
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) )?
To find the complete arc length of an ellipse find the quarter arc length (using all positive values), and then multiply it by 4.
Thanks a lot bro for your help.
thank you so much sir ❤❤
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.
best teacher ever
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.
Exactly!!
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.
You rock man !
Sir you know the importance of understanding 👍❤️
Your videos are addictive
Wow😲😲 never thought of this
I appreciate it thank you
Thanks a lot
Really nice formula !
Thanks sir .
Thank you!!!!
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.
well obviously he is assuming they are. just blown up for viewing purposes.
thank you very much
Nice intro!!
Very very good
Thank you sir
Thank you very much. 👍👍🔝🔝
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.
Thank you so much. You reminded me of using Pythagoras everywhere 🤣
Gogou theorem
Medio entiendo el inglés, pero se entiende perfectamente lo que explicas. Gracias.
Thank you! My book was not clear in how this formula came about.
Say "ruler" 10 times in a row
dope shirt @blackpenredpen
Hi, do you have a video on how to graph a cycloid and an epicycloid given a their parametric equations? thanks a lot !
This is easily the simplest way I've seen of deriving the formula.
wooow this was awesome mind blown comrade
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
Amazing
Amazingly simple
Nice!
Here is the "dL" lmao, great video!
high school me derived this formula while being in his dad's card and felt happy about it. lol.
When i was 15 ( almost One year ago) when i was making theories when i was learning university maths at same time and i discovered a Proof to this formula implicitly ( by a diferencial infinite series), but i though i discovered a new thoery but then i realized that my formula is another Proof to this formula😂😂🤦🤦 i got euforic and then depressed after that
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
?
Tnx sir ❤️
Love the Doraemon theme in the background
could you make a video deriving the arc length for polar curves too?
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)
Excellent work young man!!
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 ...
please could you do a vid about the area of a 3D curve? that should be very interesting
this boy flexin the supreme
I keep thinking he’s saying “this is the deal..”😂
Thanks for the video, but now, what about the ellipse or circle?
I think you can separate the problem is other smaller problems, for example the length of the circle is 4 times the quarter or the circle which you know is y=sqrt(1-x^2) for example. For the parabola, you have the expression of f(x)=y if you know a few points so it shouldn't be too much of a problem. For other cases like the circle where you have 2 or more images for a single x or y value, just split the problem in several little curves you can then add up and it shouldn't be too hard after this if you know the formula of the curves
whilst watching your pi function video you say that for n factorial you need to apply ) l'hospitals rules n times, what about non integer values of n? can you explain or do a video on what exactly applying l'hospitals rule e.g 1/2 times would entail?
I've done line integrals before but now I know WHY they look like that!!
Can you show that the length of the function f(x) = x ^ n as n increases without bound from (0,0) to (1,1) is equal to 2? It is visually obvious, but I could never figure out the integral to apply the limit.
this can be applied to parametric equations aswell i assume? just doing extra steps to be in "t" (if x = f(t), y = g(t)) ?
Trystan Hooper
Yes. I did that as well. The video will be up soon
Will you talk about line integrals?
Its always pythagoras that shows up everywhere, even when you dont expect it...
So when they are coming up with proofs is a part of that manipulating it to have it in that integral and dx operator at the end format ? If you didn’t have that dx at the end by factoring it out the integral would not work?
isn't L = integ (from 0 to 1) dL ?
or from n to n+1 ?