Calculus: We state and prove the First Fundamental Theorem of Calculus. Before the proof, we show the following examples: (a) constant function (rectangle), (b) line through origin (triangle), (c) f(x) = sin(x) over [0, pi], and (d) f(x) = (x-1)^2 -1 over [1,3]. The key step in the proof is to reinterpret the Mean Value Theorem. We also note the interpretation for motion in a line.
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