Arc Length

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Deriving the Formula can be seen here: • Deriving the Arc Lengt...
Arc Length - Find the arc length of a function. The basic formulas and two examples are shown.
For more free math videos, please visit PatrickJMT.com

[@kamelghouti2706]

I am a calc 2 student. And I stopped going to lectures cause I have no idea what that old fucken professor is talking about. Instead I go to the library and I look at your videos and try to understand the topic myself. Thanks a lot god bless you

[@aatra1]

Kamel Ghouti I feels you. HAHA.. I wish I did that earlier.

[@TheFunkyCriminal]

+Kamel Ghouti dude i wish i could do that, my teacher has a ton of quizzes so i have to sit through an hour of lecture without learning anything

[@aatra1]

Nick Merrick If you don't understand the lecture you'll fail the quiz so might as well just miss it too. I just missed the lecture and quiz days then went to take them after I learned it on my own. Thank God I graduated!!

[@evilwearsgucci]

+Kamel Ghouti I'm doing the same too, I learn more from this videos since calculus I than with my professors :D

[@Michael-mh6kg]

L bruh

[@steelstax]

Much respect to the creator of these videos.

[@patrickjmt]

+Josh Jeong thanks!

[@AliKayhan1]

On the last problem when you factored out the x^2 + 1/2 + 1/16x^2, your answer was( x+ 1/4x)^2. Why is his so? Because once I expanded ( x+ 1/4x)^2 I got x^2 + 1/2x^2 + 1/16 x^2

[@pravinsingh5628]

@@AliKayhan1 x^2 and 1/x^2 will get cancel in middle term

[@CaptSumTingWong1]

I learned more from this 10 min video than my past 2 lectures that are over 2 hours long... thanks college!

[@hbrockster]

Seriously you are the BEST!! I love how you explain every little step, even if it is a small addition or subtraction step. And thank you for not having a condescending tone!!!!

[@alyssawells1556]

This is literally the question I have been stuck on for half an hour god bless you Patrick still saving uni kids 11 years later

[@robrussell6303]

Made a youtube account just so I can thank you for these videos. Thank you so much!

[@ATrekafied]

I can't explain to you how great it is that you make good quality videos. I've been going over calculus 2 material since I am currently in that class. The way you explain is very straightforward and is helpful to watch right before an exam or starting my homework online.

[@yogotah]

Your videos are quick and concise, very easy to watch..and not too tedious. I happen to have a very good calc teacher, and adding the fact that I watch your video as review, this is making my math become extremely potent. Thanks Patrick.

[@saria19]

My Calculus 2 professor faces the board and speaks in very broken English. You have clarified in 10 minutes what he spent 2 hours twisting into an indiscernible mess. Thank you.

[@patrickjmt]

@ace0415 for these type, you often end up factoring and doing some sort of u-sub. in general though, it could be quite difficult. but in a textbook, these problems are set up to work out

[@samanthat.4281]

Thank you so much for posting. Yesterday in class when the AP calc teacher went over this stuff, I had no idea what he was talking about. I didn't even know what arc length meant! Now, after watching this, the concept of it seems really simple and do-able. THANK YOU!!

[@ShankGoof]

Thanks man! i missed class the day prof went over arc length. This has been a life saver, yet again! thanks!

[@krishx1688]

I freaking love you, took me a while with my studying to figure out wtf the book was talking about and you just made it SIMPLE.....

[@bodohkambing5376]

THANK YOU - I do IB and you have actually saved my maths internal assessment - I was trying to calculate the arcs of a basketball trajectory and I used parametric equations but it got weird because I had higher release angles getting shorter arcs - you're a legend, thank you

[@timothymoore6657]

I have a calculus exam tomorrow and this will probably be on the test... really love how easy these videos are to understand because I simply cannot learn in my lecture. My professor basically turns her back to the class and talks to the whiteboard the entire time, but this is so much better for me! Thank you so much, hopefully I do well on my test tomorrow!

[@daniemarie4884]

Thank you so much for posting these, Its so helpful being able to see problems done where I can pause and go back if I need to to catch something. My recitation TA goes so fast through everything and skips lots of steps so I am in a constant state of confusion in class.

[@paretcl]

You sir are the reason im passing Calc 2. Thnx soo much!!!!

[@mrreilly]

Thanks a million for this video! I had a sub for my calc 1 class for this topic and he was awful. He taught it in an hours time with the proof and one example and I didn't understand a thing. He was basically a talking text book. Ten minutes of your video made this so simple to understand! Thanks!

[@patrickjmt]

glad you like my videos :) spread the word!

[@kianfrawley8364]

Over a decade later and this dude is still saving peoples lives.

[@evanantoine2877]

You need to travel the world teaching college accredited courses. Most of us pay thousands in tution, yet still rely on your videos.... I wish the money i spent on tuition was in your pocket instead!!! Love and Light!

[@patrickjmt]

ha, i wish it was in my pocket too! :) glad i could help though

[@Saleem_RM]

I can never imagine my life without your videos. Thank you

[@kaliberto1]

My professor has a Phd in math, and I couldn't understand him! BUT YOU SIR! You explained extremely well that everything makes sense :') I am so glad you make these videos!! THANK YOU SO MUCH!!

[@Jeff1991N]

thank you. i am taking calculas II online and your videos have helped me. you are now my new proffesor

[@stardust92dragon]

Patrick You have no idea how much I love your videos... This is my second level of calculus and let me tell you, your played a huge role on my good grade in the first calculus level and for that thank you 😄😄 I will keep watching your videos...

[@lexorcised]

wish i had found you earlier! the semester is almost over and ive gone this whole time not understanding anything at all in calc 2, but this is clearing things up. will definitely have to use your videos as a resource for future math classes

[@patrickjmt]

come back any time! :)

[@tzarsman3234]

been 14 years and it's still helpful Thanks bro

[@minosmith9458]

Thanks so much for your clear explanations! Just understanding that a key objective is to manipulate the expression under the root sign into a square assisted me greatly. You have a talent for teaching and your calm manner in solving this problem was appreciated. I hope you consider continuing on in online teaching much in the manner of Khan Academy; there is a real need out there (here) for online instruction and most do not have the technique down like yourself and Khan Academy... Thanks again!

[@ajksail]

@patrickJMT Awesome!!!! seriously you are better then my tutor and my teacher at explaining... well everything!! just calmed my nerves a bunch with this video about arc length. Thanks for your help man and congrats on the kick ass wife!

[@NauTzZz]

"If you can't explain it simply, you don't understand it well enough." Albert Einstein

[@hani4153046]

Oh man I spent almost two hours on this question and I accidently found this video you just saved my life man you are officially my hero.

[@smiff0009]

Thank you especially for the part on factoring inside the radical.

[@hafshahmaulina11]

i dont know who you are. i just wanna say thank you so much. you are very helping me to finish my exam!!! it means TODAY!!!! Thank youuuuu!!!!!

[@474yx]

I got a test tmrw and I’ve been studying for like 3 days on this and I just finally understood it!!

[@mongoose308]

Thank you for taking time out of your day to do these videos. :)

[@patrickjmt]

well, that is a circle of radius r, so you can use C = 2pi(r) (circumference formula) ... in this case, divide by 2 cause you only get the top half, so answer should be (pi)*(r)

[@aven_5471]

Almost our whole class (from UST) watches your videos! We certainly need help in integral calculus. Hope we all pass our class :) regards here from the Philippines!

[@blue-pineapple]

I always watch your videos before working on the new lessons for my online school on calculus. But today, my online teacher linked your vid hahaha

[@jupiter1114]

Words cannot express my gratitude. Thanks!!

[@patrickjmt]

@quiquemoranmoyano i have been reading a physics textbook at night (how nerdy, right?!). i understand the problems but still feel unqualified to do videos about it (cause i am unqualified!)

[@Dvno92]

Thank you so much! I had not idea how I was suppose to factor those terrible polynomials! Thank you Patrick!!! God Bless you!

[@TheMasterbane]

Excellent video. I've been a fan for a year or so. Though when I watching it, I noticed that there is a useful trick when you go the 1/2's running around. -1/2 is the only number to which you can add 1 and it'll have the same absolute value (1/2). so (as 7:40 shows) if f '(x)^2 = [x - 1/(4x)]^2 = x^2 - 1/2 + 1/(16x^2) and f '(x)^2 +1 = x^2 + 1/2 + 1/(16x^2) you can automatically assume when factored it yields [x + 1/(4x)] (as 9:20 shows) as a consequence of factoring.

[@tatfr0guy]

@lucypiao on a ti 84, there should be a MATH button. in that list there should be something like fnint(. click that. Then, type in the first function minus the second, x (make sure to use the commas between these things), and the limits of integration. So, figuring out the area beween curves x^2 and sqrt(x) between 0 and one would look something like fnInt(sqrt(x)-x^2,x,0,1) this shoud give your answer. You can use the function grapher to check which goes first.

[@locomatic1991]

You are a life savor thank you for doing these tutorials and i hope you continue :)

[@Mrwiseguy101690]

Very well designed example. Extremely useful video.

[@LuLzezRoflcopter]

Great videos to watch to prepare for lecture... Or the night before the exam! Either way the vids are great!

[@MSTRH1998]

honestly, you have videos for everything i need! you rock :)

[@LoveLuckyCharms]

thanks! you are a god of calculus patrick

[@patrickjmt]

@Angelgrrl04 i have a video about u-substitutions and when to change the limits of integration

[@MrBlash93]

Thanks again Patrick

[@yosanw]

i love you patrick for doing the exact same math problem that was in my hw!!!

[@patrickjmt]

@luislaracuente you wish

[@chellepita]

Thank you! YOU SHOULD WRITE A CALC BOOK! My Calc book confused me much. I'm so glad I watched your video!

[@bepotts]

You make engineering math easy. Thank you.

[@cm_0011]

Dude, you're saving me for my Calculus exam! Appreciated :D

[@margotrutgers7635]

You, sir, helped me pass an exam. Thank you!

[@IWolfGod]

You Sir, are awesome. I love your videos!

[@rfatcakr]

patrick, Thanks to you. I passed math easily, I think you are talented about that explain something mathematically. Thanks from TURKEY :)

[@shaangoo]

You are my one and only calculus teacher =}

[@evangofourth9213]

You did that in exactly 10 minutes you absolute legend

[@ac444]

Wow, you made me feel so smart watching this because I could actually follow along, you're really good, thanks! :)

[@quiquemoranmoyano]

My friend, you are the best patrickJMT! thanks again, very very helpful. Now, if you only taught physics!

[@04civice]

@ 5:19 "It should always clearly um, always work out to be a positive number. So, if you get a negative number *sigh* Ssssomethings wrong..." Anyone else find the really humorous?

[@pendragon7600]

well actually when you take sqrt(u^2) you should write |u| anyway... It just so happens that both the functions he used in this video are positive for all values in the bounds.

[@Mekstee514]

Did u forget to add the plus one after plugging in the [f'(x)]^2 into the L formula?

[@MrM0hdhussain]

please try to do some more complicated problems

[@benjaminjordan2330]

damn youre hardcore

[@MrM0hdhussain]

Benjamin Jordan Exam problems usually are so much harder than any of textbook or Patirck videos problems

[@bendoughty1907]

Somewhat true... Textbooks have problems in them that are MUCH harder than most exam problems, but yes... he generally works easier problems in order to teach concepts.

[@NBLCKK]

Yeah textbook problems always seem to be harder than exam problems, with the basis being if you can do the homework in the book you wont have any problems with the exam itself.

[@Naaf69]

KFUPM XD

[@patrickjmt]

second semester typically

[@patrickjmt]

thanks!!

[@PhotonCherades]

Oh Patrick, you are my hero.

[@ubasta]

wow THANKS A LOT your videos are always so informative better than my professor

[@patrickjmt]

glad i am able to help : )

[@hectoralarcon4888]

Damn thank you SOOOO much, for tat last example I didn't notice that perfect square.

[@Jankin47]

Hey Patrick, it's probably too late because you've made videos on everything, but do you think you could offer general steps in the description, or summarize at the end? You normally do a pretty good job of demonstrating but it's nice to have it lain out like that.

[@charlesodigie6506]

Good work. Opened me up. Thank alot

[@LuLzezRoflcopter]

the x's cancel when u multiply x by 1/4x giving you 1/4+1/4

[@moed72]

the first question just came in my calculus exam. Exactly the same numbers !!

[@MaiValentineNaomi]

Thank you so much for these videos, they are very helpful!

[@IsaacWollam]

Taking cal 3 right now. Wish I found you sooner!

[@phynos8936]

If it's a function of y, your dx after the integrand also should have been changed to a dy. You probably know that, just hard to get everything. Great videos.

[@amciaapple1654]

I agree

[@patrickjmt]

@ninjaturtle205 cause i do not want to.

[@naut_nigel]

Thank you! I just had a problem like example 2 in class today and was kinda confused about how you got the squared function. :P

[@kenikozo]

@ninjaturtle205 The fact that he's using hands and actually writing it down makes it so easier to understand. If he was like other videos where it is typed / computerized, it's very hard to follow!

[@Dominicelz]

Thank you very much! Helped a lot!

[@LilVolume]

You're such a good person. If I was old enough I'd buy you a beer, sir. A guy who takes time out of his day to help random people who need some extra help in Calc. #boss

[@shaikgousiya2151]

thanks a lot sir. It's truly important for me

[@user-pr1ry2pr9j]

Funny enough, this was one of my homework problems. The exact same

[@Vivenk88]

Nice series of videos. Thanks for sharing :-)

[@samisiddiqi5411]

Yes those 2006 videos are helping me.

[@delahkful]

I recall you asking what videos you should do next. I think you should do harder veirson of the Calc1 &2 stuff.

[@allkristiningram]

Great video! Thanks so much.

[@littlevic785]

Thanks this really helped me out

[@hossamelsherif1767]

Thank you for your efforts

[@KillaTequilla83]

thank you so much, it may sound whiney but my teacher is truly awful, doesn't explain a thing and expects us to read the stupid book...hey thanks again this is a god send man

[@Vivenk88]

when you change the limits to the values of y, dx should be replaced by dy as well.

[@amciaapple1654]

I agree

[@inuyome1008]

Something I've noticed in a lot of problems I've worked out is that the final form is the same as the original and you insert the limits of integration... such as with the second problem you worked out, the original was y=(x^(2))+(ln(x)/4) and the end result was exactly this and you inserted 4 and 2 to get the numerical answer... is this usually what will happen when we don't have something like a Trig identity or lnx, or are there just certain ones that end up like this?

[@homework7783]

Thank you Patrick

[@navaneethmukund3013]

at 1:03 shouldn't dx be changed to dy?

[@amciaapple1654]

I think so

[@TheReal1441]

Navaneeth Mukund correct

[@giovanni101]

Thanks so much this helped a lot!

[@charlesodigie6506]

Thank you. You are very helpful

[@carlosenriqueulloa]

Dude! I love you! (and I mean that in the manliest way possible). Thank you for continuously saving my bacon.

[@patrickjmt]

feel free to mail a check : )