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

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

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[EADgbeist]

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

[Beni-rfiy]

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)

[utkarsh-wlsg]

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.

[jesus-zjl]

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.

[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.

[olehborys]

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

[幹嘛啦-id]

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

[saixmusic]

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

[evezhang]

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

[Djenzh]

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

[robbxxi]

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

[untermensch]

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

[thatosenoamadi]

This is legit the best math channel on YouTube.

[niteshkumar-otud]

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

[ManiSharma-cbtt]

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 👍

[seyitalidemir]

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

[evanbyrne]

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

[chemprofmatt]

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