Introduction to the Line Integral

[steinmath]

Fantastic. Really amazing job.

[anakmudajaman]

I Love The Video Introduction to the Line Integral It Can Increase My Knowledge

[AntoMelta]

Good, I like that you share this video Introduction to the Line Integral, I wish success always

[willamricard]

Nice Video Introduction to the Line Integral That You Share , So Very Nice Thanks You

[imegatrone]

I Really Like The Video Introduction to the Line Integral From Your

[bundawartini]

Your Video Introduction to the Line Integral Is Very Useful Sharing

[spaaceengineer]

To think I'm wasting my money by giving it to my University which in return provides me with terrible lecturers and hours of not understanding things and yet I can watch 20 minutes of Khan academy and get it straight away. Keep being amazing khan academy.

[lilj135z]

I'm sitting in my computer lab at school watching this and I finally got it. My jaw dropped and I said "Oh my God." Needless to say, the person on duty for the labs was not very happy about my outburst and kicked me out

[xspeedcube]

I enjoyed every minute of this video, even the phone ring at 13:44. :)

[poppilatesTV]

So much easirer to understand i love how you use the correct termsbut explain everythign in natural language so we can all understand it

[salehjamsaljames]

MAN, I am in love with your magical voice, goes right through to my brain!

[xMikay]

Why can't you be our professor? :)

[mysteryhendrix]

fantastic! thank you

[HereComesAntiG]

Isn't the 'change' in case of line integral denoted by dl rather than dS.

[elfrancotirador09]

@HereComesAntiG the assumption for an infinitesimal part of a curve is ds in general

[HereComesAntiG]

@elfrancotirador09

If dS is the small part of curve then then what is dl used for?

[Seracinfinity]

Fantastic!

[legendarysannin65]

geat explenation!

[thato794]

thank you thank you thank you

[atracaelo]

now i understand!!!!

[erin1061]

LOVE THIS GUY! LOVE HIM!

[ParkwayStudios]

I goto the Khan Academy :L

[itstheMAC]

These are the only videos I've ever seen with more than a hundred likes and ZERO dislikes. Impressive.

[leoncio91]

I almost feel bad for all the people who took caculus pre-youtube, the people who passed must of been geniuses lol. and pre-internet haha

[dvspirate]

You're awesome. I watch all your videos. Please keep them coming.

[Wahl899]

I'm going to watch your videos in my lectures from now on.

[Woddart]

I´ve come up with a new kind of theory wish I call citamentation of a specific function where u find out the curvechange for different kin of number r. lets say that y can be difinited as in the interval 2x-y-7x y will be changed between them.

My second theory is how to find out the volcitament av a closed curve if we know the function f(x) and the citament f(x)+C. Now we have to deal with how to find out the structure of this curve in the coordinate (0,0,0)

[vd853]

this makes so much sense. when i first learn it, i was just given the formula, and had to visualize the whole thing for myself, which made it even more confusing.

[anarchris]

my "teacher" just threw out the formula in our face and ran through it in under 2 minutes......and im paying him :(

[harishli2020]

ur lecture is just awesome........plz keep uploading videos like this......thank u...

[ROlockfl]

best line integral lecture ever !

[Grandiaangel]

It's official,

You are the greatest man alive.

[SHEEK905]

I think that a line integral is denoted by a small "s" not a large S. I believe the large S denotes a surface integral. ds = line integral, dS = surface integral.

[randomIy]

thank you. i usually have to teach myself calculus because i don't understand my professors so it feels nice to have someone teach me. thank you again.

[Nomad6763]

Its weird, i find myself nodding and saying "uh huh" to no one

[pevargas]

You sir are a genious at teaching...........thank you for your good work!

[MarvelsofaLifetime]

Wow, such a clear thought process. This is definitely one of Kahn Academy’s best videos.

[TwistedLemniscate]

Now that infinitesimal calculus can have a rigorous foundation, is there a valid reason for calculus to still be based upon limits?

Are there limitations to infinitesimal calculus when going into more advanced things? Just because we may need limits (do we?) for sequences and analysis, do we need them for calculus?

[Jekvan]

Holly tears...I think all of the lecturers around the globe want to keep the beauty of calculus to themselves,or they just get sadistic pleasure of seeing grown students literaly cry in their lectures.

This stuff right here,this is the way it supposed to be tought.Infact,it is better to kick out all of them overpaid professors and just screen this masterpiece at classes instead.

Thank you.Thank you thank you thank you thank you!!

[queopz]

One more thanks! Most important, something that's not common nowadays in teaching, "you don't give the fish, you give the tackle". Please never stop as you're really helping knowledge to be free, as it should ideologicaly allways be.

[yegentube]

Thanks for million times.

[S1CKDRIFT3R]

i love you man, not in a gay way but i would kiss you if i ever saw you

[100nassar]

Sal, Keep this up! It would have been my dream!

I'm sure you will make some comments on arc length, since your great work with line integrals practically DOES IT ALREADY!

Thanks,

--dale

[rinwhr]

wow he just derived the formula for parametric arc lengths

[colorsendinginurple]

this clears a lot up, as usual!

[BarneyTang]

thank you so much. I read the textbook over and over for a couple times, and I still could not understand the concepts. The video is so intuitive that it totally blows my mind.

[DerUnbekannte]

wow.. after many many hours of listening to my professors repeatedly explaining this, I was still in a state of confusion, 19 minutes of listening to you and I can say with confidence I now understand how this works.. thank you so much!

[KellyPedro]

Thnak you, sir. I was lucky to find your work.

[Ferrus91]

Oooh I hope you get to Green's theorem.

[SuperSTi5]

Haha amazing, I was seriously thinking "gee, I wish he had some videos on line integrals" the day you posted these. Thanks so much.

[rockYhre]

Great! It's very interesting to watch.

[Gangstaq8]

Finally ! Math is Back

[FHomeBrew]

Sal, I like your vids and they helped me get through some of my exams.

I find it sad that my attentionspan is too short to stay focussed. I can actually predict what you're gonna say and where the story is going. I'm scrolling and skipping through most of it..

Math is my life, it's the last thing I do before I go to sleep, then I dream about it and wake up with it, spending my day entirely with math.

I don't know why I find your vids not interesting enough to watch all the way through :(

[gobberpooper]

yay thanks for listening to my request on facebook sal!

[hanzabass]

This is mathematical delight for the layman. Thank you SO much

[Wurstdesmonats]

Wow.. it was impossible not to understand what you were saying^^

[norwayte]

This is the best introduction into line integrals I have seen or read.

I really looking forward for all kinds of line integrals and their interpretations. And looking for surface integrals... and Green, Stokes, Gauss.

You are literally saving lives.

[CrazyApe360]

@norwayte

I wish I could like this TWICE.

[andreiduffy]

WoW.. this is exactly what i needed. thanks