20: Scalar Field Line Integrals - Valuable Vector Calculus

Video on arc length: • 7: Arc Length of Curve...
Website that I used for visualization: math3d.org
Explanation of scalar line integrals, along with an example problem!
Valuable vector calculus playlist: • Valuable Vector Calculus
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Music: C418 - Pr Department

[@carsonwall2400]

One of the best math channels on KZbin

[@TheNickinator96]

Coming from a math major, your videos are great! Keep it up

[@aliberro]

KZbin's algorithim should make your videos present on every mathematician's device

[@briandwi2504]

Excellent video. Your channel is a real find. Thanks!

[@bonganemathebula7556]

Clear and concise...👌...A new subscriber

[@sreajan]

Very Helpful. Thanks Gentleman.

[@malefetsanekoalane4549]

Great. Thanks 🌍 from Johannesburg.

[@raselrox4115]

Thanks 🙏🙏😊

[@ratnabesra8959]

Thanks a lot

[@Study-lf6bj]

In the first part of example, at time 8:40, when you were integrating between 0,2, you took f(x) only, which equals f(t), why you did not take f(y) also, ? or is it because we are asked only for x, since z= x. Thanks

[@MuPrimeMath]

See 8:28. We're given that the function is f(x,y) = x.

[@berzerksharma]

Can you explain definite Integration of The greatest integer function? Love from India

[@MuPrimeMath]

See this video for an explanation: kzbin.info/www/bejne/a5jXl2yFqq2Ub7s

[@pariharbiceps9827]

what if the curve is a closed curve ?

[@IsmailPbx]

I don't understand at 10:25, how can a curvy line be put onto a straight surface, isn't that the reason why the map of the earth is so inaccurate. We can't put something curvy on a straight plane.

[@MuPrimeMath]

Right, and that's why taking the line integral with dx or dy is DIFFERENT from taking it with respect to ds. You're calculating a different area!

[@patolorde]

you always amaze me.

[@papanujian7758]

Such a beauty

[@maxamedmuuse4882]

beautiful explanation!

[@eulersfollower7140]

Wow ,you are doing a terrific job explaining math ,I hope that I should be fluent in math like you one day

[@khalilmathematics952]

very good explanation. the examples selection are very good

[@YahirOrihuela-k3g]

saved my life

[@divyanshdev2382]

love from India

[@bulldawg4498]

As a math purist, I'm disappointed that you resorted to "velocity" to convert ds to |r'(t)| dt when this is just a straightforward computation of arc length ...

[@celkat]

I find the *r* - *v* - *a* and | *v* | = ds/dt relationships extremely useful for intuitive problem-solving, so I'm always happy to see them put to good use :)

[@vaibhavbandal8325]

Thanks for such an amazing vedio. Can we say that the explanation given by you was solely for explicit functions 《z=f(x,y)》 ?

[@MuPrimeMath]

The method that I presented here is for integrating a given (explicit) function f(x,y) over a given 2-dimensional curve C. For some applications it might be necessary to solve for f(x,y) from an implicit equation!

[@oraz.]

The integral you get is the magnitude of the vector valued function prime with the limits plugged in?

[@rajinfootonchuriquen]

It's just the magnitud of the curved area