Changes

*[[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.

The Fundamental Theorem of Calculus says that the two operations are inverses -- to find the area under the graph of f(x) between a and b, that is, the definite integral F(b)-F(a), find the function g(x) whose derivative is f(x) (that is, find the ''antiderivative'' of f).  The area under the graph of f between x=a and x=b is just g(b)-g(a).

The Fundamental Theorem of Calculus says that the two operations are inverses -- to find the area under the graph of f(x) between a and b, find the function g(x) whose derivative is f(x) (the ''antiderivative'' of f).  The area under the graph of f between x=a and x=b is just g(b)-g(a).

As a mathematical statement the fundametal theorem of calculus read,

As a mathematical statement the fundametal theorem of calculus read,