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{{Math-h}}

{{Math-h}}

==The Fundamental Theorem of Calculus==

==The Fundamental Theorem of Calculus==

The Fundamental Theorem of Calculus, first proven by [[James Gregory]], is the rather remarkable result that the two fundamental operations of [[calculus]] are just inverses of each other.  Those two operations are performed on [[functions]] from the [[real numbers]] to the real numbers, and are most easily visualized when the functions are expressed in terms of graphs.  The operations are:

The Fundamental Theorem of Calculus is the remarkable result that the two fundamental operations of [[calculus]] are just inverses of each other.  Those two operations are performed on [[functions]] from the [[real numbers]] to the real numbers, and are most easily visualized when the functions are expressed in terms of graphs.  The operations are:

*[[Differentiation]]—find the slope of a function's graph at a given point.

*[[Differentiation]]—find the slope of a function's graph at a given point.

*[[integral|Integration]]—find the area under a graph between two given limits.

*[[integral|Integration]]—find the area under a graph between two given limits.