The Line Integral, A Visual Introduction

Vector Field Visualizer:

This video gives a brief introduction to the line integral. I talk about line integrals over scalar fields and line integrals over vector fields along with a few sample problems.

For some reason, I didn't like this video very much. It doesn't have the satisfying feel I get from some of my other ones. Even though I am extremely satisfied with the animations, I'm not one bit with the audio. I was going to redo it, but then realized I had 550 subs, and decided to upload it anyway, someone might like it.

If you want to study some more, Paul's online notes are great for breezing through the concepts, but if you want a formal course, you could either take it at a college nearby or try Khan/other online classes.

Music by ChillHop

#calculus #multivariable #lineintegral

[vcubingx]

Here's a small intuition correction: When I said "projecting the integral", that isn't particularly correct. It's more of a "stretching out" the curve so it becomes straight, without distorting its length. This is why we have the factor of sqrt(x'^2 + y'^2) in the conversion formula.
(Credit to Dr. Steve Trettel for pointing this out!)

MISTAKES! At 4:11, the problem should be (1, -1). I read it wrong and typed it wrong. Wow.
Also in the first example the integral's function should be 3(3-2t)^2-2(6-7t).
ALSO IN 8:15 I MISSED A MINUS SIGN HOLY

[theInternet]

This kinda looks like 3Blue1Brown content. Not to say this isn't awsome still.
That's more of a compliment than anything else but i'll be damned if you aren't an avid viewer of him.

[quitest]

I am a simple man, I see videos helping people to understand the concept of math, I hit like

[Miguelocod]

As an electronics engineering I needed to refresh this 6 years after taking Multivariate calculus, and this was an excellent explanation. Thanks!

[steventhijs]

There is a minor mistake at 4:50, is should just be '-2(6-7t)', not '-2(6-7t)^2'. The answer of 8 × sqrt(53) is correct though if you meant a line segment to (1, -1)

[tandlose]

This is great! I like the balance you have between questions and explanation, 3blue1brown never uses questions which is a shame because it is a nice way to apply what you've learnt and get a breather from the learning. On the other hand the examples are quick and you don't waste time explaining basic calculus so it doesn't feel dragged out and uninformative like many other math videos who uses two thirds of the time for examples. Great work and I can't wait to see more!

[Harry-ubfv]

This encouraged me to learn Vector Calculus.

[johnstone]

your parameterization for the curve C at 4:25 is incorrect. It should be 6-5t not 6-7t

[mahatmawisesa]

8:14 isn't that integral should be -3(7+5t)-5(33+39t) ?

[isaacaguirre]

I am a first year EE student studying for my vector calc exam . This is the best channel i have found this year regarding this topic. Keep it up, you're the best.

[martinsanchez-hwfi]

If C was from (1, 1) to (3, 6), shouldn't the parametrization be [3-2t, 6-5t]?

[utkarshsaxena]

Thank you for giving such details. I don't know why these are not written in books clearly, and we have to search the internet for better understanding, especially for mathematics.

[quantumleap]

the animations really helped solidify the concept, great job.

[gururajmundargi]

sir you have started to teach difficult math using animation it really helps to me.iam a engineering student from india. please dont stop uploding this kind of vedio

[fyu]

Really good but I think you make the same mistake 3Blue1Brown made when he was starting. Talk a little bit slower. But otherwise great video!

[PTGaonkar]

ತುಂಬು ಹೃದಯದ ಧನ್ಯವಾದಗಳು... ಇದೊಂದು ಅದ್ಭುತ ಪ್ರದರ್ಶನ... ಸಂಪೂರ್ಣವಾಗಿ ಅರ್ಥವಾಯಿತು...

[prathmeshpatel]

Dude this is great. It made everything so much clearer. Thank you for making this

[bostangpalaguna]

dude... your visualization is crystal clear! thank's a lot !

[sidimohamedbenelmalih]

This is the first time when I started to understand the integrals, and it was great, like a schematization to what's Waiting for me, and be prepared to it

[photon]

indians are finally making quality content.