Fundamental Theorem of Integral Calculus

This lecture covers the fundamental theorem of integral calculus, focusing on the concept of area under a curve. It explains how to calculate the area using definite integrals and provides examples to illustrate the process. The lecture also introduces the derivative of the area function and explores its relationship with the original function. Various techniques, such as the limit definition and the mean value theorem, are employed to establish the fundamental theorem's validity. The lecture concludes with a detailed proof of the theorem, emphasizing the derivative of the area function and its connection to the original function.