Line integrals: path dependence | MIT 18.02SC Multivariable Calculus, Fall 2010

[@JorgeFlores-cr5et]

Great explanation, clear examples and good teacher!!

[@JMDylan]

Thank you MIT for this video! Very clear and easy to follow. Calculus would be a lot more enjoyable if my professor was as clear as this. I should submit an application!
-Dylan Miller

[@gonzalitooo94]

i am from argentina and i can undertand this guy better than my college teacher

[@PhamVoBinhGiang]

I'm in USA and this is WAY better than my graduate teacher.

[@aristoi]

It shows the sad state of American education that this only has 3,373 views.
Thanks Joel Lewis for being an excellent lecturer.

[@lukeorlando4439]

but the whole world has access to youtube.... not just america

[@justpaulo]

On a) I found it easier to parameterize as follows:
x = 1 + t
y = 1 + 3t
with t from 0 to 1

[@watt_the_border_collie]

I did the same, using the method we learned to parameterize lines

[@burcmm]

The vector field Joel is defining is not conservative (it is not the gradient of a scalar function). I chose the parameterization as x=2t and y=4t^2 with 0.5

[@sandratobias2158]

This is very clear. Thank you.

[@thedivinehostess]

This was so helpful!

[@aldo3749]

Thank you very much! It helped me greatly.. Now I am understand it. :D

[@burcmm]

Oh duuh :) I noticed the title is "Path dependence of line integrals", then of course different parameterizations or paths will yield different answers. Hence he chose the vector field as non-conservative...

[@tshepangmakhubedu9450]

thank You ..MIT ..great video

[@milky1234123]

This helped so much

[@Luis-wz4fd]

Is it wrong to choose the parametrization: x = 1+t and y = 1+3t with t varying from 0 to 1 for the first curve, in part a?

[@ishandave3542]

no it is absolutely correct any parametrization will work just avoid non defined functions for example if x takes the value 0 do not take the parameter t such that x = 1/t.

[@cctang4922]

Your parametrization makes the calculation easier than that of the teacher does.

[@velizarhristov1838]

I did the same and I got the same result as the instructor, so I'm guessing that it isn't wrong.

[@the_eternal_student]

he did not explain how to find the equation of the line for y and x. it is not obvious to everyone. If you do not know, you can ask the microsoft co-pilot.

[@lukeorlando4439]

I thought work done is independent of the path taken.. so why is the line intergral path dependent?

[@limlinkua2529]

i like your smile before you talk anything XD

[@MrSolutions69]

+lim linkua Xd

[@euniceboafo2551]

this was helpful but you jumped some steps and it made it a bit challenging to understand

[@ricardo4fun922]

I don't see the point of introducing a new variable t, that just seems to be more work to do. Is there any particular reason for that or is it just a fancy approach ?

[@skm-yq7ny]

how to do for 3 variables

[@hyogos8796]

just parametarize a given curve using one parameter, t, as he did.

[@no_one1073]

For 3 variables you need to parametarize using 2 parameters. For example in case of sphere of radius a you need to use phi and theta.