Deriving the Arc Length Formula in Calculus

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  • Опубліковано 24 сер 2024
  • 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.

КОМЕНТАРІ • 69

  • @damian.gamlath
    @damian.gamlath 6 років тому +66

    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
    @Sabrina-sc1db 7 років тому +73

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

  • @hubenbu
    @hubenbu 2 роки тому +2

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

  • @TooMuchTigerero
    @TooMuchTigerero 7 років тому +5

    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!

  • @mariambobat3227
    @mariambobat3227 7 років тому +10

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

  • @tamircohen1512
    @tamircohen1512 5 років тому +23

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

    • @conelrad1447
      @conelrad1447 5 років тому +15

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

    • @alphamega3306
      @alphamega3306 4 роки тому +11

      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
    @TheCutieEnity 7 років тому +2

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

  • @dvscrobe
    @dvscrobe 6 років тому +1

    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
    @MercerBay 6 років тому +4

    Very clear explanation - thank you!

  • @arnaovdiwan
    @arnaovdiwan 2 роки тому

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

  • @BlackCardvbs
    @BlackCardvbs 7 років тому +2

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

  • @doaard9174
    @doaard9174 7 років тому +5

    i passed math exam successufully with your lessons .thanks

  • @professorAP
    @professorAP 7 років тому +1

    thanks a lot Patrick. you are the master of derivations

  • @mansurbhamani3905
    @mansurbhamani3905 3 місяці тому

    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.

  • @BangMaster96
    @BangMaster96 7 років тому +5

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

  • @rahimalizada6530
    @rahimalizada6530 6 років тому +1

    Excellent explanation

  • @agienugroho8544
    @agienugroho8544 Рік тому

    that's crazy sir!, thanks!

  • @Arzoo..4334
    @Arzoo..4334 3 місяці тому

    Thank you very much
    From Pakistan ❤

  • @212ntruesdale
    @212ntruesdale 6 років тому +1

    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).

  • @ahmed3746
    @ahmed3746 7 років тому +3

    thanks man,, ur the best

  • @livegamingstreanzz4441
    @livegamingstreanzz4441 7 років тому +8

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

    • @tehXfiles
      @tehXfiles 7 років тому +1

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

    • @livegamingstreanzz4441
      @livegamingstreanzz4441 7 років тому

      tehXfiles studying to become one

    • @clysen8234
      @clysen8234 7 років тому +1

      So how are you then civil engineer?

    • @clysen8234
      @clysen8234 7 років тому +7

      *Quantum physics* Two states at once.

    • @Siggfuggggg2000
      @Siggfuggggg2000 6 років тому

      how is that going for you

  • @carlosandresaveros3338
    @carlosandresaveros3338 6 років тому +1

    You're awesome dude!

  • @mysteriousraflio1143
    @mysteriousraflio1143 7 років тому +1

    Thank you!

  • @herropaul
    @herropaul 7 років тому +3

    I had just learned this yesterday in class lol

  • @sanahaskuranage8071
    @sanahaskuranage8071 2 роки тому

    well done!

  • @carloschuecos7014
    @carloschuecos7014 6 років тому

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

  • @Hobbit183
    @Hobbit183 6 років тому +1

    that was dope

  • @giovanekim4041
    @giovanekim4041 4 роки тому

    Amazing video man! Keep it up.

  • @manishkapoor800
    @manishkapoor800 4 місяці тому

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

  • @omegapolar1355
    @omegapolar1355 3 роки тому

    That was brilliant!

  • @marinimatteo9536
    @marinimatteo9536 8 місяців тому

    Bravissimo !

  • @ChrisL4310
    @ChrisL4310 6 років тому

    Amazing video! Appreciate it!

  • @user-sd2zp8xv1e
    @user-sd2zp8xv1e Рік тому

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

  • @victorserras
    @victorserras 6 років тому

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

  • @Hobbit183
    @Hobbit183 6 років тому +1

    can u do it for rotational areas

  • @Hobbit183
    @Hobbit183 6 років тому +1

    *grabs popcorn

  • @baselinesweb
    @baselinesweb 4 роки тому

    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.

  • @charnielduterte3796
    @charnielduterte3796 6 років тому +3

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

    • @patrickjmt
      @patrickjmt  6 років тому +2

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

  • @kkamous7278
    @kkamous7278 7 років тому

    thanks a lot .

  • @anilkumarsharma1205
    @anilkumarsharma1205 5 років тому

    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

  • @ankitshriniwasupadhyay2078
    @ankitshriniwasupadhyay2078 5 років тому

    Thanku so much..sr

  • @meganp8766
    @meganp8766 4 роки тому

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

  • @tajammalhussain7713
    @tajammalhussain7713 3 роки тому

    Can we take any point?

  • @anilkumarsharma1205
    @anilkumarsharma1205 5 років тому

    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

  • @anilkumarsharma1205
    @anilkumarsharma1205 5 років тому

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

  • @jonathanwood8847
    @jonathanwood8847 4 роки тому

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

    • @patrickjmt
      @patrickjmt  4 роки тому

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

  • @alphahelix5526
    @alphahelix5526 7 років тому +1

    MVTt

  • @samanthaairl
    @samanthaairl 6 років тому

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

  • @ahmed3746
    @ahmed3746 7 років тому +1

    thanks man,, ur the best

  • @anzatzi
    @anzatzi 5 років тому +1

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