Fundamental Theorem of Calculus II: Linking the Integral Function to Derivatives

This example demonstrates the key idea of the Fundamental Theorem of Calculus (Part II): the rate of change of an integral function matches the original integrand. It builds an object of the form F(x)=∫_a^x f(t)dt and uses the resulting representation to make the relationship between F'(x) and f(x) visually and conceptually clear. The main concepts include calculus in the form of the Fundamental Theorem of Calculus (Part II), integral functions, definite integrals with a variable upper limit, and the connection to derivatives. The construction follows the GeoGebra commands and objects indicated in the summary: the Integral command to define the integral-based function, Textfield to present formulas/values, and input/output objects such as F, f, a, InputBox1, B, plus area/A and text1 to show the integral’s geometric meaning (area) and label the key quantities. Suitable for advanced high school and first-year college calculus instruction, especially for lessons connecting definite integrals to differentiation.