The Fundamental Theorem of Calculus
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This animation is a dynamic representation of the area function we introduce in the standard
proof of the Fundamental Theorem of Calculus.
(See notes below.)
In proving that the derivative of a definite integral with respect to its upper limit
is the integrand, we introduce a special area function. This animation shows how the
value of that
function, which is the area of the blue region, changes as the input value to the function—which
is the x-coordinate of the moving vertical line segment—changes.