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The Fundamental Theorem of Calculus (FTC)

There are four somewhat different but equivalent versions of the Fundamental Theorem of Calculus. Note that FTCIII and FTCIV are just rewrites of each other.
FTCIII has the intuitive phrasing: the integral of the instantaneous rate of change of a quantity is the total change.

Partial proof:

We defer for a moment the proof of FTCI.
We assume FTCI and prove the other parts of FTC from it. Sample uses of FTC.
next up previous
Next: Using the mean value Up: Internet Calculus II Previous: Solutions
George A. J. Sparling 2002-01-27