Using a line integral to find the work done by a vector field example | Khan Academy

[@Seracinfinity]

You are an incredible teacher, My professor goes on and on and on and on without really saying anything :(.

[@sebastiansimon7557]

2:12 _“just to make it symmetric”_ - well… maybe not _that_ symmetric.

[@jeremielhomme8572]

Symmetry isn't always a good idea.

[@earendilthebright5402]

Try this, when you're stuck on a problem, try and think it through in your head logically with Sal's voice narrating the whole exercise

[@ninosawbrzostowiecki1892]

phew, close call!

[@jacobanteau6020]

almost drew a swastika

[@braineedly7543]

@@jacobanteau6020 whether x(t) & y(t) is movement after be moved by f or before be moved by f?

[@Spankmeister99]

At what point did you realize you were about to make a swastika with the vector field? lol, I'd say right around 2:10

[@md65000]

"I'd say" ... who gives a shit?

[@ChatGPT-]

​@@md65000 you had watched these videos 9 years ago ... I would like to know what you guys are doing today??

[@brad222dude]

but I wanted to know what (0,-1) looked like at 2:00

[@TurquoiseSnow]

it would point to the left

[@SuperGhostRider]

+brad222dude you nazi boy :D

[@101_huzefajohar7]

Hey sir, I dont know how can I thank you enough for these incredibly clear and brilliant conceptual explanations of such complex topics which I would never ever get to know a slightest thing about if not for you! Im finally gonna complete watching all your multivariable calculus playlist videos and have a great and deep understaning of these topics all thanks to you! Great respect and admiration for your work!

[@somenutjob]

wish i could get this guy to sit my exam for me

[@amandadube156]

I'll be damned.... Another study session rescued by Khan academy! How on earth did people ever learn calculus without you?!

[@adamc5478]

Amanda Lee Dube patrickjmt

[@zuesr3277]

+Adam C Sal is the best.

[@TheLadyDareDevil]

this is so great. Seriously, now I understand what the professor was talking about in class

[@f3ralp1g3on6]

math problems? better call Sal. this series is great!

[@orwxll8082]

Thank you Sal! I've been using your videos as an study tool since I was in the 4th grade; now, I'm a junior in university getting a physics degree! Cal 3 has been a bit of a struggle this semester and your videos have helped clarify things a lot! If I could give you a piece of my degree, I would!

[@Crissix100]

I can spend two hours procrastinating and staring at my textbook, or 10 min watching one of your videos. Thanks again :)

[@재순최-g8q]

9:18 you forgot the t in between cos^2 dt, isn't it supposed to be cos^2t dt?

[@2fbDJLL]

Thank you, Sal! You’re videos are so helpful!!

[@OctoberEmbers]

Gracious, we all practically owe you something.

[@dreamlanddon]

may God prosper you greatly Salman... You impart knowledge in a brilliant way...

[@braineedly7543]

whether (cos t) & (sin t) is movement after be moved by f or before be moved by f?

[@thisperson2505]

sal almost fell into swastica trap

[@owlattack1971]

So the vector field is a swastika?

[@RobbyBoy167]

I think he noticed. He was about to go into the third quadrant hahahaha

[@cowgate]

Ilectureonline is the king, but Sal is the Ace in the pack!! Thank you!!

[@trotskij4]

Nice math video for Sunday morning ... Makes your brain actually work! Much better than watching some dumb program on TV.

[@Pete-Prolly]

Thank you!! I've always wanted to understand line integrals!! Yay!! Im sooo happy!! I had a great teacher, but then C19 forced a "lecture class," (which I paid for in cash cuz I like Math & 40yrs old is not too late to learn,) into an "online class" which really meant: "good luck students. Read your book." (Which I do anyway, but still,) YOU made this comprehensible!! YOU did!! and I thank YOU, Sal!!!!! 😀😀😀

[@ruchi9917]

Shouldn't the work done be zero as the path is closed and it's coming at the same place? :/

[@MMNayem-dq4kd]

@@ruchi9917 Its not for every field.The case you mentioned is applicable for conservative field.

[@sumanthmopidevi2341]

Very clear explanation, excellent.

[@josephdauriajr.8860]

I don't know what I would do without you

[@RubenSantos-x3q]

4:34 wouldnt r(t) have to equal to sin(t)i^ + cos(t)j^? I know the final result would be the same but just to be consistent??

[@arooobine]

These videos are so helpful! Thank you!

[@latetilla0205]

You derseve to be a millionaire my friend, thank you so much for the help

[@colorsendinginurple]

makes so much more sense now. once again...

[@MrAlbashiri]

i love you khan academy.

[@luchis117]

Funny how there are some of us spending thousands on "education," when many show up here to actually learn the material well--and it's free (aside from ISP charges)

[@aSuleymanli]

thanks Sal. your videos always save my time

[@neerajdubey7481]

thank you so much dear sir you helped me rationalize intuitively the integral.

[@BoZhaoengineering]

It is Maxwell equation language about vector filed.

[@sebastiankarlsson4355]

Mr. Salman, ur vids are fantastic! Keep it up!

[@ye3068]

So helpful! Thank you

[@Abdoolkasim]

Wonderful explanation! Huge respects! I admire your teaching. Thanks a lot!

[@ChintanMeena]

Thank you master

[@jegerjon1991]

Because, when you dot to vecotors you get a scalar: (i+j)DOT(i+j) = 2

[@myfavost]

Thank you so much. So helpful! Couldn't figure out how my professor got the f(t).

[@nathi30]

thanks for uploADING /////we can apply greens theorm and calculate the result much faster

[@mindloop4070]

this applies only for non uniform circular motion else work done is zero incase of unform one

[@faizlaw4241]

Extremely Fantastic video

[@platypusperry5574]

Nicely explained

[@Incrue]

@9:10 shouldn't be cos^2 t dt ?

[@TurquoiseSnow]

you're multiplying cos(t) dt from the dr to -cos(t) from the f(t), so you get -cos^2 (t) dt.

[@julianrachele757]

Yes, he just forgot the t

[@mager56723]

do you have a video about doing this over a straight line?

[@Ray-jn7hl]

Thank you very much

[@milenahadzi-tosev9991]

so good, thank you!

[@chlaichlai123]

VERY HELPFUL

[@Johnno1979]

Could someone please direct me to an example of calculating the work done moving a particle between 2 known points? (i.e. a straight line)... just trying to get my head around a few things.

[@evanparshall1323]

When you evaluate the line integral, why don't you do the square root sum of squares of the partial derivatives?

[@randomIy]

@Hayskiller2 i think the parameters are given

[@lazypunk794]

I cant thank you enough.

[@daikonradishquotes]

thanks a lot! really helpful

[@norwayte]

Good. Better. Best.

[@sagarsahu2355]

what would be the change in solution if the path is taken clockwise. what will change to get answer positive?

[@value21value]

when you have a vectro field the vectors of i and j are free on space? i mean they haven't a fixed starting point?

[@MrJkidd07]

Aren't the i and j supposed to be switched when you defined your f(x,y)?

[@HenryEBrass]

No, at any point on the x-y plane, the y component of the vector force field is equal in magnitude to the negative of the value of the x coordinate of the point, and the x component of the vector force field is equal in magnitude to the value of the y coordinate of the point.

[@braineedly7543]

@@HenryEBrass whether x(t) & y(t) is movement after be moved by f or before be moved by f?

[@HAWXLEADER]

LOL the -2pi was obvious since the beginning... in this case the force is always tangent to the direction of motion... hence force is always -1 relatively to the path and the path itself is 2piR while R=1... great teaching as always!

[@earendilthebright5402]

cos (t) dt

[@VicfredSharikver]

very nice as usual

[@asif7240]

Thanks

[@MFGBG123]

Why does the "i" and "j" disappear when you put what f(t) and dr equals in to the integral?

[@300483rahul]

in dot product you just multiply the components to know how much of two vectors are going along same direction, which makes sense sense since work cannot have direction.

[@braineedly7543]

@@300483rahul whether x(t) & y(t) is movement after be moved by f or before be moved by f?

[@DeFordMusic]

what program do you use to make these videos?

[@gryranfelt5473]

I don't think it's very well explained at the beginning why each of those points creates the corresponding vector. If y is 1 and x is 0, wouldn't the vector go from 0 to 1 in y direction?

[@TTFMjock]

Well, then the natural question is, what causes the movement?

[@MrZajoxxx]

why are there suddenly no unit vectors when you make the f(t)*d(r) operation?

[@MrPeeepe]

Nice video, very helpfull :)

[@arjunacharya9514]

how to evaluate: integral of xdy-ydx along the circle x^2+y^2 ?

[@princeraj3975]

Use green's theorem

[@t3hb0ss]

i agree, this vector field is swastika like, very much so..

[@mtflyer05]

You were dangerously close to drawing a swastika, Sal.

[@papsanlysenko5232]

But isn’t this field conservative, so line integral over closed path should be zero?

[@avinashkarale1498]

Exactly. I too did not get it

[@papsanlysenko5232]

@@avinashkarale1498 oh, actually I figured it out. Actually it is not conservative. Try it, there is no such function F.

[@ruchi9917]

I'm thinking the same thing!!!

[@arthurdoran9722]

can't access Khan from my internet because it claims non compatability. it worked last week. there is no tools menu at the top of my browser. I'm on win 7 and MSN

[@schelias9544]

am I correct thinking that î is (1, 0) and j is (0, 1)? we had a different approach to this in our lessons, so I am not familiar with this notation

[@Reallycoolguy1369]

Yes

[@Matoro342]

i love you khan

[@SameerKhan-nd5qb]

f(x,y)=y(i)+x(j) take this as a force and post your answer in reply

[@juld55]

@Hayskiller2 Watch his videos on parametric equations.

[@jjmarcos]

Ah the classic swastika vector field.

[@roshansphotography4140]

thanyouuuuuu

[@kahalamathvidz]

i watch khan vidz for entertainment.

[@r410a8]

Why f(x,y) becames sin(t)i-cos(t)j ? I don't figure out

[@semiawesomatic6064]

You're ridiculously thorough, however, you wrote cos^2 without a t inside of it. But thanks for the example!

[@samchugh5086]

why isnt the work done 0 for a closed path?

[@CasualVloggingGoneSerious]

Thats in case of conservative force

[@samchugh5086]

vishal kumar thanks.

[@SameerKhan-nd5qb]

The force that we had isn't conservative if he had taken f(x,y)=y(i)+x(j) then this ones conservative you'll get it as zero try it once

[@braineedly7543]

@@SameerKhan-nd5qb whether x(t) & y(t) is movement after be moved by f or before be moved by f?

[@austinbeckd]

No, no, no. I would like to see the vector field symmetric.

[@josephdauriajr.8860]

I love you

[@toaster182]

Couldn't you just use Stokes theorem?

[@carultch]

Only if you are interested in a closed path integral. If you are interested in a partial path of a non-conservative field, you have to set it up this way.

[@Furzellewen]

well, he is sponsored by microsoft...