The Line Integral, A Visual Introduction

Comments · 278

• VC

  @vcubingx · 7 years ago (edited) · pinned

  Follow-up on Green&apos;s Theorem! -&gt; <a href="https://www.youtube.com/watch?v=8SwKD5_VL5o">https://youtu.be/8SwKD5_VL5o</a><br><br>Support me on Patreon: <a href="https://patreon.com/vcubingx">https://patreon.com/vcubingx</a><br><br>Here&apos;s a small intuition correction: When I said &quot;projecting the integral&quot;, that isn&apos;t particularly correct. It&apos;s more of a &quot;stretching out&quot; the curve so it becomes straight, without distorting its length. &nbsp;This is why we have the factor of sqrt(x&apos;^2 + y&apos;^2) in the conversion formula. <br>(Credit to Dr. Steve Trettel for pointing this out!)<br><br>MISTAKES! At <a href="https://www.youtube.com/watch?v=dnGDmZynvYY&amp;t=251">4:11</a>, the problem should be (1,-1). I read it wrong and typed it wrong. Wow. <br>Also in the first example the integral&apos;s function should be 3(3-2t)^2-2(6-7t).<br>ALSO IN <a href="https://www.youtube.com/watch?v=dnGDmZynvYY&amp;t=495">8:15</a> I MISSED A MINUS SIGN HOLY

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• TH

  @theInternet633 · 7 years ago

  This kinda looks like 3Blue1Brown content. Not to say this isn&apos;t awsome still.<br>That&apos;s more of a compliment than anything else but i&apos;ll be damned if you aren&apos;t an avid viewer of him.

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• MA

  @mahatmawisesa9706 · 5 years ago (edited)

  <a href="https://www.youtube.com/watch?v=dnGDmZynvYY&amp;t=494">8:14</a> isn&apos;t that integral should be -3(7+5t)-5(33+39t) ?

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• QU

  @quitest4850 · 6 years ago

  I am a simple man, I see videos helping people to understand the concept of math, I hit like

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• ST

  @steventhijs6921 · 6 years ago

  There is a minor mistake at <a href="https://www.youtube.com/watch?v=dnGDmZynvYY&amp;t=290">4:50</a>, is should just be &apos;-2(6-7t)&apos;, not &apos;-2(6-7t)^2&apos;. The answer of 8 × sqrt(53) is correct though if you meant a line segment to (1, -1)

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• MI

  @Miguelocod · 4 years ago

  As an electronics engineering I needed to refresh this 6 years after taking Multivariate calculus, and this was an excellent explanation. Thanks!

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• HA

  @Harry-ub2fv · 6 years ago

  This encouraged me to learn Vector Calculus.

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• JO

  @johnstone6848 · 7 years ago

  your parameterization for the curve C at <a href="https://www.youtube.com/watch?v=dnGDmZynvYY&amp;t=265">4:25</a> is incorrect. It should be 6-5t not 6-7t

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• KR

  @krulusgaming1061 · 5 months ago

  i am amazed that people are getting all this stuff ... you all are something...

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• IS

  @isaacaguirre1881 · 2 years ago

  I am a first year EE student studying for my vector calc exam . This is the best channel i have found this year regarding this topic. Keep it up, you&apos;re the best.

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• TA

  @tandlose · 7 years ago

  This is great! I like the balance you have between questions and explanation, 3blue1brown never uses questions which is a shame because it is a nice way to apply what you&apos;ve learnt and get a breather from the learning. On the other hand the examples are quick and you don&apos;t waste time explaining basic calculus so it doesn&apos;t feel dragged out and uninformative like many other math videos who uses two thirds of the time for examples. Great work and I can&apos;t wait to see more!

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• PR

  @PrateekNarainMishra-g7x · 9 months ago

  Correction!<br>Dot product gives the extent of how parallel two vectors are. <a href="https://www.youtube.com/watch?v=dnGDmZynvYY&amp;t=382">6:22</a>

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