Is there any geometric explanation of relationship between Integral and derivative?

Asked Sep 09 '14 at 21:37

Active Dec 05 '19 at 23:37

Viewed 1,848 times

It is said integral is anti-derivative, derivative is tangent of graph function in each point on the function and integral is the area of the region in the $xy$-plane bounded by the graph.

I can not understand the relationship between these, can anyone help me? I want understand the relationship between area and slope of tangent line.

edited Dec 05 '19 at 23:37

sam wolfe

3,465

asked Sep 09 '14 at 21:37

J.J

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Possible duplicate. – Hakim Sep 09 '14 at 21:38
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You can think integral as a sum or accumulated value (in the sense of distributions) and derivative the representation of each member of the sum. Its easier to see taking finite intervals instead of infinitesimals. – Sep 09 '14 at 21:44
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I imagine most modern calculus textbooks (the thousand-page monsters) have a few pages devoted to intuition for this point. Probably near the "Fundamental Theorem of Calculus", which should be listed in the index. – GEdgar Sep 09 '14 at 21:52
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possible duplicate of Why is the area under a curve the integral? – Antonio Vargas Sep 09 '14 at 23:31
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@Hakim The linked question focuses on why integral is area, and to the extent that the answer relates areas to tangents the explanation isn't geometric. – Conifold Sep 10 '14 at 00:10
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@Conifold Yes, but it links it to differentiation at the same time. – Hakim Sep 10 '14 at 12:18
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The youtuber 3blue1brown has a video called what does area have to do with slope, he explains intuitively and geometrically the relationship. here's the link https://www.youtube.com/watch?v=FnJqaIESC2s – Donlans Donlans Dec 06 '19 at 05:12

Is there any geometric explanation of relationship between Integral and derivative?

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