What is a LINE INTEGRAL? // Big Idea, Derivation & Formula

[@jesus-z9j6l]

I am a college student from China.Honestly speaking,there are lots of Calculus videos in Chinese webs,but no one can rival yours.Thanks a lot.

[@utkarsh-wl8sg]

Trust me If I had a teacher like you, I would't miss a single class. Your way of teaching makes maths fun and not just some problem solving methods and calculations on a notebook. Thank you sir.

[@hydropage2855]

I am from the United States and trust me, you guys always say “I am from India” immediately. Why? What does it have to do with anything?

[@utkarsh-wl8sg]

@@hydropage2855 you are right. I don't know why do we do it. But may be to let content creaters know a little about their global viewership.

[@Beni-rf8iy]

You are a fantastic teacher, the fact that you are able to make it so simple shows how much you understand. (it applies for the other videos as well)

[@howmathematicianscreatemat9226]

Yeah, it shows he understands both the topic and the way his students learn. Rare combination

[@olehborys1462]

No one destroys calcukus lecturers in uni so well as Dr. Trefor. This is on high level.

[@BoZhaoengineering]

I especially appreciate how the concept gradually unfold and the time and derivative respect time get in to play. A great interpretation about line integral.

[@Orotachi]

Greetings from India ! Really appreciate the teachings which are making my understanding of the subject a lot better.

[@DrTrefor]

Glad they are helping!

[@saixmusic9322]

I'm trying not to cry while in the library I've been trying to understand this for so long and in a couple of minutes... there it is! Oh my god thank you so much

[@thatosenoamadi8497]

This is legit the best math channel on KZbin.

[@DrTrefor]

Thank you!

[@幹嘛啦-i2d]

Can’t imagine that people before learn these stuff without ur help, definitely tough for them.

[@flowersArePretty1]

Thank you so much Dr. Bazett, because of the visualization and intuitive description I actually understand what the line integral represents, at first I didn’t even know what I was trying to actually calculate!

[@robbxxi]

seriously thank you for formatting this in a way that makes it easy to understand what’s actually going on behind these integrals

[@seyitalidemir4455]

this channel is one of the best channels i have ever seen about calculus

[@DrTrefor]

Thank you!

[@derrickhsieh8032]

Super underrated channel! Definitely will recommend. I would go more into why I love this channel but I have to study for a Calc 3 midterm!

[@DrTrefor]

Much appreciated!

[@Djenzh]

I love how enthusiastic this man is! It's almost contagious

[@untermensch787]

You're an absolute hero, this makes so much sense, I wish regular teachers were as helpful as you are

[@peasant8246]

Best explanation that I've seen of this idea. Great work!

[@evanbyrne7020]

You have no idea how helpful this video has been. Thank you so much for the stuff that you do.

[@niteshkumar-ot4ud]

This channel deserves at least 5 million subscribers. This channel is painfully underrated 😔😔

[@DrTrefor]

I hope it gets there ha!

[@chemprofmatt]

What a beautiful introduction to a rather tricky concept. Your choice of example makes the concept far more clear than any textbook could.

[@thehighground583]

I would just like to say THANK YOU for making the conceptual explanation walk hand in hand with the visuals. That was something I had hoped to cover more when taking calc 3 and it helped so, so, much.

[@ManiSharma-cb5tt]

So grateful to have someone who teaches the concepts in such a great manner 🙏✨✨

[@महिमापुनःआनयन्तु]

Man, it is so difficult to imagine what is line integral but after this video it's very clear . Thank you 👍

[@evezhang9596]

YOU ARE A GENIUS! I am going to remember the snow bank example for life.

[@Skv112]

only 99.3K subs ! there should be 10M subs for the quality of teaching you are providing.

[@DrTrefor]

So close!

[@BHUCampus]

Very helpful Love from INDIA🇮🇳🇮🇳🇮🇳❤️❤️❤️

[@vijaysinghchauhan7079]

You made me feel the subject.

[@fredericoamigo]

Super impressed by the vids in this series. Really well explained and visualized!

[@DrTrefor]

Much appreciated!

[@mattdivoooo]

@@DrTrefor I was gonna say the same thing. Your visual aids are intuitive, and I wish watched this 2 years ago when I was in Calc 4. This is top notch!

[@sushimeng]

Sir you are definitely helping me pass Cal3. Thank you so much for making these well-explained and visualized series!

[@borntobereal2004]

This made my day! All of my friends were struggling with this and l was so scared but luckily yours is the first video l stumbled upon and now l have a crystal clear concept of this!

[@elielsilva7432]

Man this is so cool. I was searching for some videos to learn about this topic in spanish but there are only people telling you the formula of the integral and making the calculus straight up, but I really wanted to understand the concept before digging into the exercises and this helped me so much. Thank you a lot!

[@edmund3504]

Wow! Great video. I've been refreshing some Calculus III material since it's been about a year since I've taken the course and your videos are really helping :)

[@DrTrefor]

Great to hear!

[@JustinsRealmMC]

You're really saving my class. THank you ^_^ I always love intuitive introductions!

[@DrTrefor]

Glad they are helping!

[@computersciencestudent1129]

The way you present the material makes so intuitive and easy to approach. This by far the best explanation for line integrals i have seen out there . Automatic subscribe from me, you got me hooked . Thanks Doc !

[@bablubhaskar1223]

I owe you my life professor, you just saved my semester, thank you.

[@bobbymcgeorge]

Oh Brother Trefor you have done it again - many thanks! Another superb compliment to Lectures 19 & 20 MIT 18.02 Multivariable Calculus.

[@maryrubin9072]

Thanks!

[@DrTrefor]

Thank you so much, I really appreciate that!

[@iusedtobetoxic4752]

Thank you so much sir, you explain everything to the root and even give examples! Great for us students who aren't fortunate enough to have a teacher with an explaination style that fits us.

[@rorro6281]

This videos are awesome! Greetings from Chile

[@yz2039]

Really appreciate the content you created! I learnt calc back in undergrad, but I forgot so much. Your videos helped me to pick up and extended original knowledge base. Thanks!

[@novelas3536]

Another banger. Your teaching style is so good.

[@JohnVKaravitis]

One of the most informative KZbin vids ever.

[@innovationsanonymous8841]

This stuff makes a lot more sense when muliple youtube professors explain it to me and draw me some pictures. Thanks for relating it to arclength.

[@fahadshoaib8735]

Greetings from Pakistan! These visualizations really help to make sense out of these equations. Appreciate your work.

[@WenyingXu-g5r]

Such a great tutorial! Thank you for explaining things soooo clearly.

[@christintkunjumon3262]

man u r a lifesaver, I have studied this topic in college for about a month and did not understand a word, but this video has made this concept way easier, thnx a lot man

[@dwaipayansharma2282]

@Christin Kunjumon That's why I don't attend college lectures...Khan Academy and This channel are more than enough

[@mkh6338]

Your explanation made the concept way easier to understand. Thanks a lot

[@timothykelebeng5230]

I didn't realise how much I didn't understand until I watch this. Thank you

[@ricardoalvarez4976]

12:00 hey guys just a tip, this can be also written as the integral of f(g(t),h(t)) . |dr/dt| . dt or the integral with respect to t of the function parametrized, times magnitude of the derivative of vector function with respect to t

[@sadeedaq]

How did i not find this channel man i loved every second of it instant subscribe

[@GoutamDAS-ls1wb]

The best visuals and explanations I have seen so far. Immensely helpful for Calc 3 (II) refresher I am taking currently with edX. You were meaning when "k goes to infinity" instead of "n going to infinity"--but all of us understood!

[@robpatterson2861]

Oh my goodness! You are the coolest! I can't wait to be smart enough to get into this! Totally fascinating they way you sell it! Thanks!

[@sarvanray3971]

I m really wasting my time and money in college . U r an irreplaceable gem sir

[@GreyAreas]

absolutely fantastic explanation!!

[@DrTrefor]

Glad it helped!

[@schizoframia4874]

This video made me feel smart

[@maryjanechang414]

Great series! Your enthusiasm really makes this better

[@DrTrefor]

Thank you so much!

[@Eduardo-cr8ri]

Prepping for the GRE and didn't get a good grasp of calc 3 thanks for these vids dude

[@ilangomahalingam7159]

Thank you very much for your time and effort.

[@edidiongedemeka2096]

I have to commend you for your graphical representations, they are much appreciated

[@Deepak-pi9xx]

Thank you. You saved my time. You explained well in less time.

[@DrTrefor]

Glad it helped!

[@abhijeetkar1306]

love from bangladesh sir, your videos helped a lot to understand the topics deeply. keep doing the good work.

[@Darkness_7193]

Snow analogy is so good. I surprised that Trefor didn't connected blue curve and circle with half-transparent barrier and then didn't said "This is snow height about what I was talking!"

[@HoangNguyen-yb9ki]

Wow. Just wow. I got A for every single undergraduate maths course but still impressed so much by your visualization. I plan to study a master degree in mathematics next year, so I have a question that I hope you don’t mind to answer. My question is: “Is it possible to visualize maths at graduate level like what we can do with calculus, probability density function and linear algebra? “ Thank you very much for your lectures. And by the way, if you want to commercialize your courses in higher maths, I would be a loyal customer. I would be happy to pay $500/course(I think it’s reasonable price, compare to online courses in Actuary).There are so few intuitive yet still rigorous maths course online. MOOC are just too easy, and recorded lectures from universities are just too dry and lack of visualization.

[@DrTrefor]

Not even concept, but yes trying to visualize and have clear mental pictures is super important all the way through grad school

[@anishsharma6702]

WOW ,great got a simplistic understanding in detail to such an important topic,THANKS

[@aman_theCodeAddict]

You ideas to explain line integral was awesome and i like it

[@DrTrefor]

Glad you liked it!

[@aman_theCodeAddict]

@@DrTrefor I send this to all my friend in my college

[@bulldawg4498]

Educational & instructive ... Excellent presentation!

[@mallelavarshith2811]

The way ur teaching is awesome sir 😊

[@triplemav1588]

This video really helped me visualize what I was calculating when I was doing the calculations. Thanks a lot your explanation was very thorough and helpful!!

[@samuelhawksworth1923]

Excellent video

[@nikhilyewale2639]

Nice video, as always! 1) It would be even nice to point out that, the pythagorean thing can be written simply as | r'(t) | , and that | r'(t)|.dt denotes the infinitesimal arc length. 2) I hope you also add in coming up section , the line integrals of a vector field.

[@DrTrefor]

Good point. And of course it's the same thing, but some texts also write it as |v(t)|. Anyways, I"m launching a whole series on vector calc so line integrals in vector fields are definitely coming:)

[@nikhilyewale2639]

@@DrTrefor Is it also possible show that line integrals are independent of the parametrization, using visualization ? Please include in the series if possible :)

[@李郅杰]

you taught so good, keep doing it.

[@DrTrefor]

I appreciate that!

[@frangaray8979]

Great explanation! It helped me a lot. Saludos desde Argentina!

[@DrTrefor]

Glad you liked it!

[@aldotovar9231]

it's nice to know you're now a doctor. Props!

[@DrTrefor]

Haha been one for five years, but finally got around to changing the channel name:D

[@IlIlllIlll]

Very helpfull, thank you!

[@Ferdimitry]

Dr Trefor, u r simply the best. Do you have a textbook? U make mathematics an interesting series to watch 😜! I always look forward to ur videos. Thank you for making life a bit easier.

[@DrTrefor]

I'm actually working on some this semester. Soon I'll be release my differential equation playlist (it's coming after vector calc) and that one IS going to have a custom, free, open source textbook. After I do that, I kind of want to go back and make maybe not textbooks but more like workbooks for some of these courses.

[@rin-or3no]

@@DrTrefor I am sorry to ask this but will these youtube videos and text book remain free for next 1-2 years?

[@SAAARC]

@@rin-or3no pretty sure they're gonna be free lol

[@ananiassepuru7819]

@@DrTrefor Great Idea. I think a workbook would be very helpful .it would be a great way to test ourselves

[@nila-333]

Loving your classes. Thank you thank you 🙏❤

[@emtnan1733]

Understood and practical 👏🏻

[@somanathdash3153]

Thanks sensai, you helped me again

[@htchtc203]

A very good introduction of the line integral. Thanks.

[@DrTrefor]

Glad it was helpful!

[@prashanthkumar0]

😍😍😍😍amazingly explained as always.. love from india 😊

[@DrTrefor]

Thank you!!

[@emilwang8818]

Extremely underrated.

[@markpadley890]

First class explanation

[@xaitpri7905]

Thanks a lot sir 🙏, respect from🇮🇳

[@Alannnn14]

I'm from Brazil, I am doing a physics major at UNB ( universidade de Brasília ). Thank you for your videos 👍

[@DrTrefor]

cool! Good luck in your degree:)

[@freshely9309]

THANK YOU SO SO SO MUCH! your videos, explanation and everything is perfect for me! instant subscription :D You are great at explaining things.

[@DrTrefor]

Thanks for the sub!

[@akkpariyaram6786]

Thankyou so much for the amazing explanation:)

[@DrTrefor]

You're very welcome!

[@fazlerabbi5622]

Awesome awesome awesome. So concrete and so specific

[@Uknon78]

Finally i understand line integral

[@farhatfatima1168]

Thank you so much sir for making us clear our concept and visualization helps us alot in understanding the concept of line integral

[@chrisc884]

this man is a goddamn war hero - engineering/compsci/physics/chem/math students, 2021

[@ManishKumar-gw4qw]

it is awesome to learn visually and your explanation is great 👍

[@DrTrefor]

Thank you! 😃

[@sergiorome42]

I loved this derivation, simple, consise, and beutiful

[@VirajPatel-y3f]

Amazing video, and very well explained. Thank you!

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Amazing seriously outstanding Keep it up :)

[@buh357]

This is so beautiful. Thank you.

[@harshitgaur9968]

You are a genius Respect 🙏

[@subdano9638]

Thank you sir, you helped us too much.

[@satiou7064]

Thank you so much it is really well explained

[@astrobruce7585]

Awesome explanation sir!

[@willm6598]

omg this video is incredible!