Multivariable Calculus | Line integrals over vector fields.

By way of a physical application, we derive the notion of a line integral over a vector field. Some examples are also given.

[giovannimariotte]

On the other hand, this is just the best video ive found explaining this captivating concept

[SliversRebuilt]

Michael you are the man dude, thanks for everything 🤙🏻🤙🏻

[giovannimariotte]

Great job. But one question, there doing the integral we are finding the work, of course, but geometrically spealing we are just like measuring the distance of the curve in this field. Or, on in other words we are like weighing the field at each point and then doing the entire sum ??? It would be awesome if you clar me up this doubt

[antoniocosta]

At 13:59 the final result should be 18t^2 + 16t - 4.

[joyofmath]

Antonio Costa found, I think, the first error (13:59 the final result should be 18t^2 + 16t - 4.), but there's also @ 15:02 18*5 = 96, rather than 90.
We've all been there ... many times.
Also @ 15:34, should be -62t
Doesn't change the meat of the concepts, just arithmetic, the least interesting part.

[KSMK]

I don't understand why it's written as F(r(t)) while parameterizing F(x, y)

X=g(t), y=h(t)
Function of t s
It should be written as F(g(t), h(t))

r=g(t)i+h(t)j
dr/dt=g'(t)i+h'(t)j
dr=r'(t)dt

Vector line integral=Int_F(g(t), h(t))r'(t)dt