In this lesson on the Fundamental Theorem of Calculus, we learn about the terminology and symbolism involved in integrals, such as the integrand and differential. We also explore the Average Value Theorem, which states that there exists a number c in the open interval a, b, such that f of c is equal to the average value of f over the interval. Finally, we delve into the derivative of phi, which is the function defined by integration, and how it relates to the Fundamental Theorem of Calculus. Examples are provided to illustrate these concepts.
Average value theorem. The function p(x) = integral of f(s) ds. The fundamental theorem of calculus.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.