Introduction to the line integral | Multivariable Calculus | Khan Academy

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Introduction to the 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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Khan the savior of university students 

ddsslse
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why cant some math professors teach like this? i sit in a math class for 1.5 hours and scratch my head. i watch Sals video for twenty minutes and makes total sense.

lonelywuffy
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I am in my 2nd year at college studying advanced Mathematics.And this is the first time that I have actually understood the reason behind doing integral f(x)dx. Teachers usually associate Calculus with mugging up the formulas and doing tons of numericals, but nobody even bothers to teach the theory behind it all.And the sort of explaination that you give cannot be found in the books.Kudos to you.This is just phenomenal.

inflamedwithrage
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13 years later, still the best explaination video on line integral.

amandeepsaha
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I shouldn't be paying my university as much as what I do considering the fact that I'm always on Khan Academy

Bond
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your example of finding the area of a weirdly shaped wall just made this instantly click for me before an exam, you're my hero right now

sabretoothstudios
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He is soooo good. Stewart's Essential Calculus can't even compare to this 10 minutes of common sense explanation. Thank you!!

mariedrapalova
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This video taught me in 20 minutes what my professor failed to teach me in more than 2 hours.
Sal Khan is the best!

isaac
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In my personal experience, you are the only teacher that has never failed to provide an intuitive understanding of math! Thank you so much!

noctua
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I'm sitting in my computer lab at school watching this and I finally got it. My jaw dropped and I said "Oh my God." Needless to say, the person on duty for the labs was not very happy about my outburst and kicked me out

liljz
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I can’t fathom the magnitude of my appreciation and the depth of my gratitude for this.... there aren’t simply enough words to express whatever it is I feel.... thank you

omealyjackson
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OMG...
You genius...
Not one of my professor could teach me like

djflmdlwqlf
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Do you know that pleasure you get from understanding the nature of something and seeing its genius? This video fits this perfectly. Thank you, Khan Academy!

phylton
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I have read explanations from 3 different books and many articles trying to understand the logic behind the line integral and none of them explained it that well as you did. This makes so much sense! Thank you!!!

sofiiadruchyna
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registered to class and stay at home watching this may be a more joyful college experience

yuzhewang
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Thanks so much Sal. You always reminds me why I chose to study math.

biaaaa
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this makes so much sense. when i first learn it, i was just given the formula, and had to visualize the whole thing for myself, which made it even more confusing.

vd
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you're the man! Thank you very much sir, it was mind-blowing I finally understood linear integrals!

edoardogribaldo
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He draws so perfectly even on a computer, Respect.

fozansharfulhaque
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Amazing. Was completely confused until I watched that! Thank you.

shane