Fundamental theorem of calculus

The fundamental theorem of calculus is the statement that the two central operations of calculus, differentiation and integration, are inverses of each other. This means that if a continuous function is first integrated and then differentiated, the original function is retrieved. This theorem is of such central importance in calculus that it deserves to be called the fundamental theorem for the entire field of study. An important consequence of this, sometimes called the second fundamental theorem of calculus, allows one to compute integrals by using an antiderivative of the function to be integrated. In his 2003 book (page 394), James Stewart credits the idea that led to the fundamental theorem to the English mathematician Isaac Barrow although the first known proof of the fundamental theorem was due to the Scottish mathematician James Gregory.

Related Topics:
Calculus - Differentiation - Integration - Continuous - Function - Fundamental theorem - Antiderivative - Isaac Barrow - James Gregory

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