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cask1
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Hi, this is a newbee question. Does the Fundamental Theorem of Calculus supply a visual (graphical) way of linking a function (F(x)) with its derivative (f(x))? That is, the two-dimensional area under a curve in [a,b] for f(x) is always equals to the one-dimensional distance F(b)-F(a)? If you graph x^2 and 2x, they look nothing alike, and there’s no clue as to how they are related, but the area from 1 to 2 under the curve y=2x is always equal to (2)^2 – (1)^2. The units work out also.