Line Integral - Physical meaning

We relate a concept in mechanics with the line integral and that is the line integral gives us the work done by a vector field on moving a point along the curve C.

Check out www.gaussianmath.com for an indepth study and more calculus related lessons.

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• donny
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[bballniket]

isn't it true that the force of F in the direction of D is F (dot) D only provided that the magnitude of D is 1? if not, the project of vector F onto vector D is not equal to the dot product...is this correct?

[donylee]

bballniket,

I know what you mean. Went to take a look and it turns out that I can't seem to give a concrete answer. You are right in saying that to get the projection of F in the direction of D, D needs to be unit, i.e. normalized dr/dt. However, I believe that the integration will 'take care' of the calculation so long we are integrating w.r.t to correct parameter.

That is, dr/dt int. w.r.t t or dr/ds int. w.r.t s (arc length).

I did an example with t and s and it works both ways.

[apat472]

You definitely explained this better than my teacher, but I'm still confused as to what the line integral is.

[donylee]

Hmmm,

In short, and let's see whether I can compress the meaning into a line:

It is a way of finding the sum of a certain quantity, in this case the vector field, over a curve which is given by a vector equation.

[donylee]

In short, and let's see whether I can fit the meaning into a line:

The line integral is a way of finding the sum of a certain vector quantity, in this case the vector field of say electric charge, magnetism or gravity, over a curve given by a vector-valued function.

(Any mathematics rigorous practitioners can correct me if I'm wrong)

[hnaiker]

can you post linear algebra course (matrices and solving different forms echlon ets ets ..) thanks i have a midterm next week and i dont understand anything the professor says in university

[donylee]

Hello Hnaiker,

I would love to teach a linear algebra course, though I must say that is one of the more difficult topics for me to learn, hence it won't appear anytime soon. I do hope you did well for your mid-term.

I just uploaded 17 videos on Fourier Analysis. Hope that will help in the futuer.

[ohmannhey]

Dude ... fantastic!

But one question ... Could you numerate the videos as to give them an order ... so that we know where to start and where to go next! Thanks!

[V8decimator]

you are the bomb. i go to a major university, ang you explain this stuff better than any of my professors.

[xjiang4]

@V8decimator what major university? This video sucks

[Cryogenetics]

Wow, this was really helpful! For the past few weeks i've been doing line integrals but I was never really sure what any of it meant. This video was really instructive. Thanks so much!

[MHUnited1]

Your a good teacher. Explained integral concept quite easily for someone with an art background.

[gr0mithtimon]

nice job but do the world a favor and stop saying 'okay?' at the end of every sentence D:

[azngreenteas]

Please keep this up. U r a really good teacher!!! this really helped!

[DoubleDutchBust]

9:59

[spike86IL]

I have a question. Why would you integrate F*R' instead of F*R'/||R'|| ??

I was thinking you would integrate the force dot with the unit vector of velocity rather than with the velocity vector itself.

[Kerpal2253]

Awesome vid.

[satranifan]

@maijib2009 he's from Singapore I believe....he has a site too gaussianmathematics or something, he's pretty cool. he's no professor, but he does know quite a bit of useful math eh?

[Gello81]

Hey great explaination, lol I always was curious why we would use variable t in line integrations