The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus
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Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at
Average value theorem. The function p(x) = integral of f(s) ds. The fundamental theorem of calculus.
  • 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?
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.
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Reviewed by MathVids Staff on December 19, 2008.
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