Arc Length

[judosinger]

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.

[METHEDIST]

what do you do if the problem is y^2 + 2y= 2x +1.. i dont know how to do this problem thanks

[METHEDIST]

@METHEDIST and the range is from (-1,-1) (7,3)

[torbir69]

i love you

[ninjaturtle205]

Why dont you use a notepad software? Just like the guy at khan academy does. That way your hand wont come in between.

anyways thanks

[patrickJMT]

@ninjaturtle205 cause i do not want to.

[ace0415]

sooo.... what do i do if the equation doesnt end up being a perfect square under a square root? I've been running into this more often

[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

[8644371]

YOU. ARE. AWESOME!

Seriously. These videos brighten my day!

XD

If it weren't for you, I'd be stuck at precalc level, scratching my head at what my prof is failing to teach. You rock!

[cjisavailable]

i wish you weren't left handed lol jk... i cant see what you are writing... i still love you... can you adopt me please or can i be your younger sibling D:

[nuigurumisama]

genius.

[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

[elnulan1]

How's physics coming for you? I don't take it until next semester, sure would be nice to have your help.

[Apocsapel91]

I understand that having advertisements on your videos helps you keep making them, but if you could please refrain from having advertisements in the middle of your videos, it would be greatly appreciated.

Besides that, I love these videos. They help me more than any professor or TA ever did.

[tastescrunchy]

@Apocsapel91 shut up.

[Gargola11NoTa]

patrick do Physics!!!!!!

[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!

[hicelina]

How am I supposed to know that x^4+2x^2+1 is equal to (x^2+1)^2 ? I understand that it is the same thing... but I don't think I would've caught it on my own... is it just experience or is there a trick? - Thanks for all of your videos btw :D

[hleix27]

@hicelina experience

[hleix27]

@hicelina experience

[Nogoals92]

you are easily 10x better than my college professor at teaching this stuff.

[harismokhtar]

hye,i m not really sure actly,but when we change the x=g(y) at 1:23, shouldnt we change the 'dx' to 'dy' also at the back? can somebody explain a little bit..tq

[stven007]

@harismokhtar

yeah i was thinking the same thing. its probably just a simple mistake...its supposed to change to dy.

[streetracer8705]

Your Awesome!

[MarcoOrBust]

What are the common problems people make on the second example you solved?

[david4shure]

nic of time!

[UKCJF]

What TI-84's really need is a "patrickJMT" button.

[mooseman427]

I could not figure out this one of the problems shown in this video and I needed to for my test. You just saved my life you sweet sweet man.

[Jeff1991N]

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

[bruins007bond]

at the end, shouldn't that be (1/4)ln|4x|, when you integrate 1/4x?

[nonococo92]

@bruins007bond no cuz 4 is already out ;)

[lucypiao]

Hello, Mr. patrick: You video is very helpful and I watch it 2-3 times. I have one question that other can not answer me, I mean my school Math tutor can not answer, I wonder if you can help me.

I am taking calcuIus 1. I have two functions given, and I need to find the Volume of the area which created by these two function intersect. Now my question is HOW CAN I USE TI-84 CALCULATOR TO CONFIRM MY ANSWER??? THANK YOU!

[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.

[Oblisk47]

You make engineering math easy. Thank you.

[quiquemoranmoyano]

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

[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!)

[aboxwithoutsides]

@patrickJMT who determines your qualified? Those idiots in academia? some piece of paper? If you can do the problems you can do it!

[dotc277]

@patrickJMT lol i think you should just wing it!

[melikeydatt]

@patrickJMT Funny thing is that even if you are unqualified, you would probably still teach Physics better than my professor.

[braveheart792]

quit talking about your wife and ask her to do her own mini series of math tutorials! such as how to find the area and length of an arc when given the graph and no function :)

[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!

[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.

[pilarngaw]

pls. help me finding the length of the function g(x)=sqroot of x between the points (1,1) and (16,4) on its graph.

[superjokerrr]

@pilarngaw thats just the same with f(x)

[patchesohola]

mathematical badass

[radesh0430]

interesting......

[isasukarno]

whats the arc length of y=2x^2 where 0<x<1. can't seem to integrate it. thanks.

[BoySurvivor]

@isasukarno If i'm not mistaken this one requires a trig substitution. x=(1/4)tan(u) i think.

[locomatic1991]

You are a life savor

thank you for doing these tutorials

and i hope you continue :)

[scarykidbryan]

lol I liked how you said "somethins wrong." haha

[C4CJW]

Thanks a lot man! this stuff really does help :)

[DiMAN23]

8:34 my ass its usually a perfect square :P

thx for vid

[gaint404]

Thank you.

[socalmusic09]

nice ring

[patrickJMT]

thanks : )

i assume you mean the one that my beautifully beautiful and mathematically amazing wife gave me... she kicks ass

[luislaracuente]

@patrickJMT I thought you were gay :-)

[patrickJMT]

@luislaracuente you wish

[cessnan121pp]

I normally don't need these math videos, but my current Calc professor only writes the proof and then does random examples and moans about how hard they are. I understood the easy ones, and even the trig ones, but I never thought of factoring those ugly ones, and because of your video I managed to and got the desired answer! Thank you so much!

[JarOfBuckeyes]

Great, except in the beginning if you were to measure the arc length for x=g(y) then you would also need to change your dx to dy, which you did not show.

Just a heads up for the math students watching this video. You need to make sure that you say dy if you are going to integrate with respect to y. My math teacher marks me down for not showing that part and yours probably will too.

[cooleoe]

@JarOfBuckeyes

I agree, otherwise the equation doesn't make sense (assuming you can even grasp the concept of the equation itself lol)

[AndrewDeLong]

Holy sh*^!!!

I missed my Calc 2 class last week (an hour long) that covered this and like two or three other topics. In just five and a half minutes, you pretty much clarified everything I was worried about missing!

Thank you soooo much!!!!!!!!!!!!!!!!!!!!1

[TheMike169]

thank you very much and hopefully this zz5 test wont kick my ass

[abolibnan]

gd luck for mcmaster students in the math test zz5

[xjimmy10x]

lmao mcmaster engineering loves patrick

[HernandoEcheverri1]

hello patrick, my friends and i have been watching your videos all night. We think you are the best calculus teacher on the internet, i think you are a lot of help to many students in the world, you should come to teach at our university you ll be a great colegue.

[ErikBackelin]

hey i just wanted to thank you because i didnt knew this topic very well and your are awsome! i wanna meet you lol

[bawangrebus]

wow... I have the same question.... for the 2nd example.. really odd!!!! maybe, just maybe.. my prof gets this problem from here.... ㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋ

anyway!! awesome!!! I get this now ^^.. thank you so much for your explanation, it is a big help for my midterm ^^!!!

[TFitty2020]

Wow this matched my homework problem exactly. What are the odds?

[stuhfooyou]

thanks!

[cc69cc]

gracias

[woodenjaw]

At time 6:42 why can't you get a common denominator and combine the fractions then square square it. It would simplify the answer dramatically.

I spent about 30 minutes verifying our steps were equivalent. :)

[UFcrcjrdexter]

i wish you were my professor!!!

[redsava]

His tests would be hard :p  just cause no prof is perfect

[haymayday]

Thank you SO MUCH for the amazing help!!

[RAFAMAXXX]

easy thing. thanks to you.

[ThePaolaification]

you are the best!!!!!!

[KellyMacCornmac]

I'm still having a bit of trouble with this... on one of my problems I have

y = x^(5/6)+1/(10x^3). (from 1 to 4)

dy = 5/(6x^(1/6))-3/(10x^4)

1+dy^2 = 25/(36x^1/3)-1/(2x^(2/3))+9/(1­00x^8)+1

I can't seem to factor it.... I tried using my calculator, but it has been running for at least an hour trying to factor it.

[teamoferforever]

I'd been looking for some help and this definitely helped A LOT! thank you!!!

[856956sinewavetones]

Is this how you measure curves?

[yychoco91]

when u multiply out (x+1/4x)(x+1/4x), doesn't that leave u with a 1/2 x^2 instead?

[rejectedbrownie]

NO.

x is in the denominator.

[eltotoX]

Dude you're using the wrong hand! haha thanks for the help =)

[LeenVicious]

This is by far so much better than the way my teacher explained it. You make it so simple. I think my teacher likes to power trip and laughs when the class doesn't get it. Thank you. I wish I found your site sooner.

[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

[jordiargomaniz]

thak you very much! you make things eassier

[hassanf001]

What is your email?

I need some more help

[patrickJMT]

hire a tutor

[gnrlherpes]

@patrickJMT rofl

[AbyssZomG]

I should be giving you my tuition money :) Thanks again!

[patrickJMT]

feel free to mail a check : )

[Janelikesphysics]

Hey. Thanks for your help.

[jacobbis4lovers]

Do you see arc length in calculus two or three?

[patrickJMT]

second semester typically

[jacobbis4lovers]

In calculus one?

This stuff isn't too bad once you get the hang of it. Thanks for posting your video.

I noticed on your website that you tutor college and high school students in the austin area. Do you think maybe one you will be able to tutor around the dallas for worth area? I live in Allen and I can't find any tutors around here, you're seriously the only tutor I can find and it sucks that you live far away because you can't tutor me.

:/

[patrickJMT]

i doubt i will ever hire people in dallas/fort worth...sorry!

[AtlantiXYL]

how come you always explain better than teacher? it's true! while I am in the class I just can't get what the teacher say.

[patrickJMT]

glad i am able to help : )

[Mizumi17]

because teachers spend most of the time showing how and why the formula works. which is helpful i guess, but people tend to learn better by seeing it in action and in applications. which is what he is doing.

i always youtube the section of the book im working on lol. especially for linear alg.

[smiff0009]

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

[littlevic785]

Thanks this really helped me out

[tigernov6]

What was written at 6:55 could be used to determine the factorization of the integral at 8:43 for this problem. This is the usual method used to accurately predict the factorization of this type of problems.

[skaterceo]

can you please post a vid to find the arc length of y=e^x

0 ≤ x ≤ 1.

its pretty tricky

thanks!

[rks4sm]

this is kewl way to attract young minds towards maths!

good job!

[5iftyse7en]

isn't it suppose to be 1/4 ln |4x|?

[perhgfgb]

he is taking the integral of (1/4x). So, we can say that (1/4) is a constant, so that is the same thing as (1/4) * the integral of (1/x). The integral of (1/x) is ln|x|, so the integral of (1/4x) is 1/4 ln |x|

[jessy0516]

dude u rock!

[patrickJMT]

thanks!!

[BiGFuKeR69]

very nicee, thanks!

[sphiedd]

intervals r & -r

[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)

[sphiedd]

well i got one for u whn one is looking for the arc length of a semicircle y=square root of r^2-x^2, to see if u can explain that one to me

[sphiedd]

cool man understood perfectly,unlike my ficking profesor -_- bitch ass mexican, do u have more videos , cause u good at his man

[patrickJMT]

ha : )

[ubasta]

wow THANKS A LOT

your videos are always so informative

better than my professor

[madisonthanh]

great job :)

[patrickJMT]

thanks!! : )