Is it a theorem that "the area under a curve i.e., basically the integration is an inverse process of slope at a point on curve i.e., the derivative" ?How does one intuitively visualize it. Is there some lucid explanation, if possible in a form of proving this theorem. thanks.
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2The Fundamental theorem of calculus? – PM 2Ring Oct 18 '17 at 07:30
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This 3blue1brown video explains it nicely. – Arthur Oct 18 '17 at 07:39
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@PM 2Ring is the relation between derivative and area under the curve is the fundamental theorem of calculus? or is it that the area under the curve is the integration. please clarify – user12345 Oct 18 '17 at 07:49
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The fundamental theorem can be expressed in various ways. Basically, it says that integration and differentiation are inverse processes, so to compute the area under a curve we need to find the anti-derivative of the function of the curve. – PM 2Ring Oct 18 '17 at 08:45
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I want the simplest proof of this theorem. every theorem has at least 1 proof – user12345 Oct 22 '17 at 16:41