First Part of the Fundamental Theorem of Calculus Example
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AP Calculus AB Applet Collection
This example illustrates the geometric meaning of the first part of the Fundamental Theorem of Calculus, showing the relationship between definite integrals and the increment of antiderivatives. It involves core concepts like definite integrals, antiderivatives, vectors, and polygons. Constructed using GeoGebra commands such as Point, Textfield, Integral, Vector, and Segment. Suitable for high school students and calculus beginners.
GeoGebra Commands & Parameters
Point(xAxis) → APoint(xAxis) → BTextfield(g) → inputBox1Integral(f, a, b) → gallonsVector((x(B), g2(a)), (x(B), g2(b))) → difvecSegment(Ga, (x(B), g2(a))) → difdotSegment((-2, g2(a)), Ga) → g0seg