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This theorem proved what had
long been suspected, that under certain conditions of continuity and
differentiability, the operations of differentiation and integration
are inverse operations. If f(x) is a differentiable function, and F(x)
is any antiderivative of f(x), then the derivative of F(x) is f(x),
and the integral of the first derivative of f(x) is f(x) + c, where
c is an arbitrary constant.
As is so often the case, Newton
routinely gets credit for the FTC, although many historical documents
seem to establish that it was first proven by Isaac Barrow, around 1655.
The theorem solidified the
perceived relationship between integration and differentiation, clearing
the way for the rapid development of Calculus concepts throughout the
rest of the 17th century, and into the 18th.
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