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

My Vector Calculus playlist: • Calculus IV: Vector Ca...
A line integral - sometimes called a path integral - is an accumulation of something along a curve (again sometimes called a path). In this first video we will really focus on a curve living in 2D, with a height above that curve, and answer the question of what is the surface area that results? This will be four first major application of line integrals. The plan for this video is to introduce the big idea of line integrals, come up with a sensible definition using Reimann integration and breaking this problem into a lot of little rectangles, and then finally deriving a formula that let's us compute this easily.
0:00 Intuitive Idea
1:39 Geometric Picture
5:12 Motivating the Definition
9:30 Deriving the Formula
11:50 Line Integral Formula
OTHER COURSE PLAYLISTS:
►CALCULUS I: • Calculus I (Limits, De...
► CALCULUS II: • Calculus II (Integrati...
►MULTIVARIABLE CALCULUS (Calc III): • Calculus III: Multivar...
►DIFFERENTIAL EQUATIONS: • How to solve ODEs with...
►DISCRETE MATH: • Discrete Math (Full Co...
►LINEAR ALGEBRA: • Linear Algebra (Full C...
OTHER PLAYLISTS:
► Learning Math Series
• 5 Tips To Make Math Pr...
►Cool Math Series:
• Cool Math Series
BECOME A MEMBER:
►Join: / @drtrefor
MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: www.amazon.com/shop/treforbazett
SOCIALS:
►Twitter (math based): / treforbazett
►Instagram (photography based): / treforphotography

[@EADgbeist]

Is that Riemann sum correct at 9:06? I was expecting 'n' to be the upper bound on the sigma.

[@DrTrefor]

oh great catch, yes of course!

[@schizoframia4874]

@@DrTrefor lol

[@chconstans4630]

you actually understand what this means jeez bravo

[@gn6691]

@@chconstans4630 so you didn't understand that?

[@mistadude]

@@chconstans4630 it makes sense tho

[@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

[@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.

[@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.

[@Orotachi]

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

[@DrTrefor]

Glad they are helping!

[@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.

[@robbxxi]

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

[@evanbyrne7020]

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

[@vijaysinghchauhan7079]

You made me feel the subject.

[@chemprofmatt]

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

[@Djenzh]

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

[@sushimeng]

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

[@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!

[@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!

[@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 !

[@user-yn2me9ee9t]

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

[@user-fs1gs3px7t]

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

[@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.

[@user-oy1fj4th2e]

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

[@BHUCampus]

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

[@skvsatish5277]

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

[@DrTrefor]

So close!

[@untermensch787]

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

[@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!

[@bobbymcdingdong]

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

[@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!!

[@ManiSharma-cb5tt]

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

[@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!

[@mkh6338]

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

[@edgbaston149]

Loving your classes. Thank you thank you 🙏❤

[@JohnVKaravitis]

One of the most informative KZbin vids ever.

[@novelas3536]

Another banger. Your teaching style is so good.

[@anishsharma6702]

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

[@subalgebra]

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.

[@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!

[@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!

[@bulldawg4498]

Educational & instructive ... Excellent presentation!

[@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!

[@buh357]

This is so beautiful. Thank you.

[@olehborys1462]

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

[@bablubhaskar1223]

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

[@evezhang9596]

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

[@josequaxo6532]

Superb Explanation

[@samuelhawksworth1923]

Excellent video

[@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!

[@edidiongedemeka2096]

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

[@fazlerabbi5622]

Awesome awesome awesome. So concrete and so specific

[@ilangomahalingam7159]

Thank you very much for your time and effort.

[@niteshkumar-ot4ud]

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

[@DrTrefor]

I hope it gets there ha!

[@astrobruce7585]

Awesome explanation sir!

[@sadeedaq]

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

[@JustinsRealmMC]

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

[@DrTrefor]

Glad they are helping!

[@vaiterius]

Great explanation!

[@rorro6281]

This videos are awesome! Greetings from Chile

[@maryjanechang414]

Great series! Your enthusiasm really makes this better

[@DrTrefor]

Thank you so much!

[@willm6598]

omg this video is incredible!

[@GreyAreas]

absolutely fantastic explanation!!

[@DrTrefor]

Glad it helped!

[@abhijeetkar1306]

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

[@emtnan1733]

Understood and practical 👏🏻

[@mallelavarshith2811]

The way ur teaching is awesome sir 😊

[@fahadshoaib8735]

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

[@timothykelebeng5230]

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

[@Eduardo-cr8ri]

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

[@sarvanray3971]

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

[@studynight5414]

EXCELLENT 💫✨

[@kirankumarjinka6610]

nice explanation of the concepts

[@seyitalidemir4455]

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

[@DrTrefor]

Thank you!

[@user-iu2il6np5y]

extremely informative clip

[@ravneetkaur9652]

Amazing seriously outstanding Keep it up :)

[@baocaohoang3444]

Thank you. Your video is great.

[@farhatfatima1168]

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

[@mathemagic9070]

Outstanding explanation sir i ❤ it

[@jakirsarifmondal3466]

Outstanding !❣️❣️👍

[@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

[@somanathdash3153]

Thanks sensai, you helped me again

[@satiou7064]

Thank you so much it is really well explained

[@htchtc203]

A very good introduction of the line integral. Thanks.

[@DrTrefor]

Glad it was helpful!

[@jen8802]

Your videos are awesome! Thank you :)

[@js7244]

Thanks! really good explanation! keep doing it please!

[@MdAnik-og5sw]

Very helpful. Thank you, Sir

[@sergiorome48]

I loved this derivation, simple, consise, and beutiful

[@subdano9638]

Thank you sir, you helped us too much.

[@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

[@Deepak-pi9xx]

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

[@DrTrefor]

Glad it helped!

[@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!

[@markpadley890]

First class explanation

[@jayanthromale3389]

I always like your stuff and teaching skills sir

[@DigitalOutlawed]

Thanks so much Prof.

[@jagsproduction]

Well explained

[@tasninnewaz6790]

Man : Hey Trefor, Why not get more views on your video? Trefor : Because I don't make videos for view.

[@scholar-mj3om]

Excellent💯💯

[@richardneifeld7797]

Great video!

[@IlIlllIlll]

Very helpfull, thank you!

[@xaitpri7905]

Thanks a lot sir 🙏, respect from🇮🇳

[@arnavbhavsar8567]

amazing as always

[@DrTrefor]

Thank you!

[@user-ge8qw8gb9u]

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!

[@harshitgaur9968]

You are a genius Respect 🙏

[@akkpariyaram6786]

Thankyou so much for the amazing explanation:)

[@DrTrefor]

You're very welcome!