Fundamental Theorem of Calculus Example

This lecture illustrates the importance of the fundamental theorem of calculus by providing an example with the function F(x) = x² over the closed interval [0,1]. It demonstrates the process of calculating primitives of continuous functions and emphasizes the practical significance of the theorem in computing these primitives. Through a detailed explanation and visual aids, the instructor shows how to calculate the integral of F(x) using a regular partition of the interval, leading to the conclusion that the primitive function G(x) = (1/3)x³. The lecture concludes by establishing the continuity and differentiability of G(x) on the closed interval [0,1], highlighting its classification as a C1 function.