Line integral example 2 (part 1) | Multivariable Calculus | Khan Academy

[@petuncha]

Its so cool how math never changes. This video could be 10 years old and still helping people in 2020 to learn calc 3.

[@blexaarron]

Spring 2017

[@lfc4lyfe1998]

Winter 2018

[@adamcummings20]

Spring 2018

[@asherjunaid7847]

May 2018!

[@trollfootballgeneration8645]

October 2018

[@saadhassan9469]

Sal is the best Maths teacher. He gives such a nice intuition.

[@markolazarevic4209]

Thx man your explanations are very useful. The explanation in the text book I am studying this from are really confusing and incomplete. You are making this much more easier to understand. Keep going good job

[@renzo9063]

I'm in grade 12 and somehow trying to wrap my head around this and I feel like I am almost there. It is just difficult to visualize x+y² and I am not a big fan of geometric equations, but these videos are very helpful!!!

[@cookieMo2]

I love the colorrrssss :D made me happy :P

[@wreynolds1995]

If this was given as a problem to students, it's a bit vague as to whether or not they'd be given. The difficulty of the problem depends partially on that. In practice, here it makes no difference since this problem builds upon what we know from the last problem, where we had a similar parametrization.

[@jewbinson]

At 0.25 you say "if I graph this when y = 0" but then you draw the line y = x. But surely when y = 0, we get f(x,0) = x which implies that z = f(x,y) = x (I don't see how f(x) = y) I don't see where the line y = x comes from, please can you explain?

[@piyushrawat3862]

If now you have the answer please tell.

[@piyushrawat3862]

yes I have the ans....that is not a straight in x and coordinate rather it is a straight in x and z coordinate when y=0 in the function z= x + y^2 hence x=z

[@googlesong8679]

He definitely draws it wrongly. When y=0 the line should stay at x axis.

[@proberts411]

Yes sir. It's an infinitely thin sheet from the upper bounding curve or plane to the lower bounding curve or plane. It's essentially the integrals you did in two dimensions, but the "plane" that it is traveling in can be bent into three space.

[@elbodi9894]

thank u sir i didnt understand anythin about this until i see this video and now i can progress

[@laxgirl2016]

i'm still confused--are his parametrizations given? or do we need to parametrize the curves ourselves?

[@findinggod4561]

It is given by the way wht r u doing now

[@oyster4545]

❤❤sal the best person in the world

[@047yashpandey7]

all the videos are very useful

[@saiouln.8060]

You're my hero XD!

[@matteofioretti02]

2024 still here. Best explanation ever.

[@OsirusIrdia]

You are amazing!

[@bobmarleykagan1]

Fascinating video than you very much. But "ds" that you showed was wrong, it must be on the 2 dimensional plane not on the third...

[@binibakos1342]

bro, ngl, you better than our Prof, he is taking his salary for nothing and making maths complicated

[@mohamedelsaeed9180]

God save you brother❤️

[@kungman190]

Thank you very much for your reply I now understand what it means

[@LuisVasDeCamoes]

the drawing is confusing in this clip

[@jkinsella]

Here's a clearer graph: www.wolframalpha.com/input/?i=graph+f(x,y)+%3D+x+%2B+y%5E2

[@mohammadshahidmunir2884]

I think the drawing is really outstanding the deliverer has used different colors to enhance our understanding and to remove confusion he has used simple example and ways to help us understand as far as possible

[@rushikeshnet4you]

The function itself is little bit complex than previous video

[@LaureanoLuna]

@@jkinsella That's for z=xy^2, not z=x+y^2.

[@kungman190]

Thank you Ahfjo!

[@StiegeNZ]

Aw, I'm sad that more people haven't watched these... Ya think Sal will ever do some quantum physics stuff?

[@NTMihaila]

Fascinating! I've been out of math for a while, and clearly I've been missing out. This is really enjoyable.

[@Ahfjo]

The outline of an object like your hand, a tree, the earth, etc.

[@rialdoroeloffze628]

Please don't give my lecturer any crazy ideas.

[@muneebgillani6179]

fabulous

[@juanpablodt]

If my teachers had said that simple statement you just said I would not have the need to watch this videos for my final.

[@MrBrew4321]

Bad graph sal. You said when y is equal to zero as you drew the line y is equal to x... take the whole thing and rotate it so that line is the x axis.

[@andybuck9261]

why do you set y=2t and x=t

[@mertyigit4093]

why x = cos2t and y = sin2t

[@matheuscardoso1]

Cause if u square it and sum them, it equals R². Which means it is a circunference with R=2

[@theopenfamilychurch9951]

What would the question look like if written?

[@RileyJade99]

Is your integral of the curve correct? You have the integral of -4cos2t= -2sin2t, but shouldn't it be positive? There is a negative sign in the double integral formula you used, and the integral of cos is negative sin, so it should cancel and be positive. Or am I missing something?

[@duaimrahim1718]

the integral of cos is positive sin

[@LaureanoLuna]

The very making of the drawing is confusing. He should have drawn the parabola z=y^2 on the yz-plane and then make its vertex slide along the line x=z. This is really not like him.

[@LaureanoLuna]

@@alejrandom6592 Really smart on your part: It follows that no inaccurate stuff can be confusing.

[@ninoblones8911]

In simple words, Line Integral is simply an AREA? Is that correct?

[@amanagrawal2554]

Yes,in general.

[@ryujinryuk]

how do u get the circle with radius 2 ?

[@lucycalder8061]

the diagram is confusingly drawn - it makes no sense to me at all visually

[@kungman190]

what is a contour means?

[@comprehensiveboycomprehens8786]

9:02 :)

[@kapjoteh]

Why is y=0 what you said but y=x what you drew

[@MrBrew4321]

stupid youtube wont let me post a link but you can graph it to see im right

[@MrBrew4321]

blah blah blah

[@nagarmalsharma9992]

Shut the hell up Einstein

[@3V3RYI]

It was 1 of the most 'beautiful' video I have seen. When things are so beautiful, it becomes SEXY!