Line integral example 1 | Line integrals and Green's theorem | Multivariable Calculus | Khan Academy

Concrete example using a line integral

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Multivariable Calculus on Khan Academy: Think calculus. Then think algebra II and working with two variables in a single equation. Now generalize and combine these two mathematical concepts, and you begin to see some of what Multivariable calculus entails, only now include multi dimensional thinking. Typical concepts or operations may include: limits and continuity, partial differentiation, multiple integration, scalar functions, and fundamental theorem of calculus in multiple dimensions.

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[sajidullah]

tell u the truth..i studied this in 1975 and am now 59...Now I understand the damn line integral.

[dreia]

It's fantastic how you summarize a one hour lecture in 15 minutes

[ChrisSudlik]

Thank you so much, these videos are about to save my education. I was struggling with line and surface integrals, and some physics electromagnetic stuff, The past few videos were great, and I really get the stuff now. It is really a great thing you are doing for people.

[thehorizonchaser]

If only I watched these videos before I started cramming for finals... Learning is so much easier when you aren't stressed haha

[HAWXLEADER]

tip: try to hold shift while drawing a line to make it straight!
it should work on all drawing applications...

you are a master of teaching!

[erikmcguire]

I wish my professors would teach like this!

[fahadnazir]

This video traces the journey of a super crazy integral becoming a super easy integral :-)

[Sherlock]

It seems strange to me but even when I feel sleepy and I see his lectures I can understand even then!

[MisterTutor]

I used that method as well.

sin(t) cos(t) can be integrated to -1/2(cos(t))^2 or 1/2(sin(t))^2. The answer comes out the same both ways.

[theludvigmaxis]

Amazing job. I haven't even started calc 3 yet but I like to jump ahead. Very nicely done it managed to click and I have a very good understanding in line integrals now!

[LucifertheAtheist]

Thankyou ever so much sir. This whole YouTube teaching programme of yours is extremely benevolent. Thankyou.

[goon]

makes perfect sense. I don't really feel like seeing the advanced proof if I understand.

[karan]

at 10:53, for small method we can multiply and divide by 2. so integral part will be 2sint*cost that is equal to sin2t.then integration of sin2t= -cos2t/2 .

[Seracinfinity]

You have a real gift for teaching.
Very rare

[NiiAryee]

Line integral delivered in simple logical math. Amazing!

[tomasiscool]

@pmcmena1 no because he reordered the bounds to fit the u function; at the end of the video it wasn't "from t=0 to t=π/2", but rather "from u=0 to u=1".

[parag]

this video explains how radon transform work in ct scan...
thanks a ton..u made such a complicated thing as easy as it can be...

[sandracordoba]

Your teaching abilities are beyond normal humans. Muchas gracias!

[nikhilgarg]

WAY OF EXPLAINING STUFF IN A SIMPLE AND LUCIS MANNER

[dreia]

thank very much, you are an amazing teacher