The Fundamental Theorem of Calculus
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Lesson Description:
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.
Additional Resources:
- The Function Integral of f(t) dt - Practice with The Function Integral of f(t) dt.
- The Fundamental Theorem of Integral Calculus - Practice with The Fundamental Theorem of Integral Calculus.
- Table of Integrals - Table of a bunch of different integrals.
- Special Functions - Integrals of some special functions.
- Differentiation Identities - Limit definitions of the derivative, Fundamental Theorem for Derivatives, and rules of derivatives
Questions answered by this video:
- What is the Fundamental Theorem of Calculus?
- What is a dummy variable?
- What is the average value of a function on an interval?
- What is the minimum and maximum value of a function on an interval?
- What is the Average Value Theorem?
- What is the Mean values theorem for integrals?
- What is an antiderivative?
- How do you compute an integral?
- What is antidifferentiation?
- How do you find the area bounded by a graph?
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Staff Review
This video starts off with a review of some terminology and symbolism in Calculus, such as the integral sign, lower and upper limits, the integrand, and the differential. Some theorems and results are discussed, and finally we get to the Fundamental Theorem of Calculus. Then, some variations of the Fundamental Theorem are discussed. Some examples are also computed.
