Deriving the Arc Length Formula in Calculus

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! this video, I show how to derive the formula that is used to find arc length in Calculus.

[@damian.gamlath]

The unfortunate epitome of modern-day tertiary education is "learn elsewhere but pay us anyway" - Patrick, you help maintain the status quo. Thank-you.

[@Sabrina-sc1db]

I'm procrastinating from doing my maths homework by watching your maths videos

[@pi17]

Meh..... Yes lol

[@samisiddiqi5411]

Lmao

[@TooMuchTigerero]

I've been done with calculus classes now for almost two years but I still sometimes click on your videos just cause they're awesome! Keep up the great vids, students everywhere are grateful for your easy to understand/follow explanations!

[@hubenbu]

This is my first math analysis lesson, it's beautiful. There are so many brilliant and generous people out there.

[@mariambobat3227]

Patrick : Ensuring that we pass our Courses. You are the best.

[@tamircohen1512]

Can someone explain why the f(x_i*) turns into a regular f(x) in the last step?

[@conelrad1447]

cause the dx is getting infinitely small, so it literally doesnt matter what the difference between x and x* is

[@alphamega3306]

x_i* is a point along f(x) between x and x+ delta x. The limit as delta x goes to zero results in x = x + delta x, with x_i* between. So it’s the squeeze theorem, where the three values become the same at the infinitesimal limit.

[@TheCutieEnity]

thank you patrick. I have graduated from university and your channel have been my savior!

[@BlackCardvbs]

Patrick thanks for these lessons helped me with a lot of situations ...your the best

[@dvscrobe]

This was a very good explanation! I have a problem in Calculus where I was asked to find the distance traveled of a robotic joint. Used this to refresh on finding arc length of curve segments.

[@MercerBay]

Very clear explanation - thank you!

[@professorAP]

thanks a lot Patrick. you are the master of derivations

[@giovanekim4041]

Amazing video man! Keep it up.

[@ChrisL4310]

Amazing video! Appreciate it!

[@carloschuecos7014]

Patrick, all your videos are excellent. By the way, do you have something about deriving the radii of curvature? Thanks for all your videos.

[@rahimalizada6530]

Excellent explanation

[@arnaovdiwan]

this was a savior at midnight.....damn...thanks

[@agienugroho8544]

that's crazy sir!, thanks!

[@ahmed3746]

thanks man,, ur the best

[@carlosandresaveros3338]

You're awesome dude!

[@omegapolar1355]

That was brilliant!

[@mysteriousraflio1143]

Thank you!

[@anilkumarsharma1205]

if we have function and its derivative then we have a ration between them so we multiply this by 100 to find percentage, will this percentage gives some specific correlation between curve length of both or of function, if this method gives us some calculations then we will stop bothered about sharemarket updown

[@sanahaskuranage8071]

well done!

[@insomnia20422]

the point with the Riemann Integral close to the end was new to me, so no way i could have derived it by my own :(

[@BangMaster96]

Hey Patrick, can you please do tutorials on Discrete Mathematics it would be really helpful thank you

[@baselinesweb]

The whole part about the mean value theorem...could you replace that by dividing both delta X^2 and delta Y^2 (under the root) and then multiplying by delta X^2. You get the same result of 1+(delta Y/delta X)^2. Thanks for the video.

[@The_Professor123]

can u do it for rotational areas

[@mansurbhamani3905]

Perhaps you may make another video to find volume of Diesel Tank (cylindrical lying horizontal on the ground along it's length) as it gradually gets filled up at any instant.

[@The_Professor123]

that was dope

[@marinimatteo9536]

Bravissimo !

[@doaard9174]

i passed math exam successufully with your lessons .thanks

[@kkamous7278]

thanks a lot .

[@meganp8766]

exsubuy, whysubuy XD! great video thank you so much for explaining!

[@ankitshriniwasupadhyay2078]

Thanku so much..sr

[@Arzoo..4334]

Thank you very much From Pakistan ❤

[@anilkumarsharma1205]

is their any percentage like formula so we know that if function is given then we found the length of the curve as a frictional part of the equation try this phenomenon on a function which exist ever or the curve of the equation and total number of powers of every terms of the equation, try this at least ones

[@herropaul]

I had just learned this yesterday in class lol

[@ReinaldoDiaz1]

Me too haha

[@kryokin9771]

Me three!!! :O

[@victorserras]

Thanks for the rigorous demonstration; much better than khan academy's bs proof

[@livegamingstreanzz4441]

I AM CIVIL ENGINEER AND I had just learned this in class today .. thankyou patrick love from pakistan

[@tehXfiles]

are you a civil engineer or are you studying to become one

[@livegamingstreanzz4441]

tehXfiles studying to become one

[@clysen8234]

So how are you then civil engineer?

[@clysen8234]

*Quantum physics* Two states at once.

[@Siggfuggggg2000]

how is that going for you

[@anilkumarsharma1205]

if function is circular then what happened, means having a knot or loop type

[@reesebonin9890]

Do top half and double.

[@The_Professor123]

*grabs popcorn

[@212ntruesdale]

This is my favorite application of Integral Calculus. Breaking up the curve, g(x), into segments allows use of the Pythagorean Theorem, provided they are short enough. Then the hypotenuse equals the segment. I write dl = sqrt (dx^2+dy^2). Then I just pull out a dx using distributive property and square root rule, sqrt ab = sqrt a x sqrt b. Then I have a product, f(x)dx = dl. Now integrate both sides. What is often overlooked, not understood, is that the summation is of area under a curve, not of lengths. Yes, we want to sum the segments, but Integral Calculus doesn't do that. It just sums areas, f(x)dx. Nonetheless, using just basic math, the integral can be formed. That's very cool, as is the fact that the length of the curve, g(x), is given by the area under another curve, f(x).

[@manishkapoor800]

So thats what they used while finding the perimeter of ellipse . I seeeeeeeeeeeeeeeee . Thx a lot

[@charnielduterte3796]

I thought something happened to his index finger. It was just the red marker lol

[@patrickjmt]

i, in fact, have red marker on my hands right now :) it is often there

[@tajammalhussain7713]

Can we take any point?

[@alphahelix5526]

MVTt

[@user-sd2zp8xv1e]

If you were right handed this wouldn't be an abomination to society

[@jonathanwood8847]

Excellent video, but I cannot stand the sound of Sharpie on paper

[@patrickjmt]

seems like a lot of people don't like it. i personally like it :)

[@samanthaairl]

why couldn't you just make it as simple as possible and just use numbers ?😭

[@patrickjmt]

because that would not work

[@ashraymallesh2856]

this is as simple as it gets...

[@ahmed3746]

thanks man,, ur the best

[@anzatzi]

Can someone explain why the f(x_i*) turns into a regular f(x) in the last step?