I am aware about the Riemann sum and how they can be used to approximate the area under a curve. As the length of the rectangle(dx) approaches zero the sum of area of rectangles give the area under the curve. However none of the explanations seem satisfactory enough about why is the area under the curve related to the antiderivative of the function.Is there any intuitive explanation I can use to understand the same?
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The explanation is the Fundamental Theorem of Calculus, which is not a trivial result (sometimes people try to make it sound obvious but it’s really not). Google this, watch youtube videos on it, and spend time thinking about it :) – peek-a-boo Jun 20 '25 at 08:22
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Of possible help are these Stack Exchange questions/answers: What is the best way to intuitively explain the relationship between the derivative and the integral? AND Iconic image to explain the fundamental theorem of calculus? AND Why does the fundamental theorem of calculus work? [already cited above] AND I need a (very) intuitive explanation of fundamental theorem of calculus – Dave L. Renfro Jun 20 '25 at 11:15