As the name suggests, the Fundamental Theorem of Calculus (FTC)
is an
important theorem. The theorem connects integrals
and derivatives. There
are two versions.
Version 1
Define
where f(x) is a continuous function. (This assumption can be weakened.)
In
other words, F(t) is simply the area under the f(x) curve from a to
t. The
Fundamental Theorem of Calculus states
There is an analogous result for indefinite integrals. Let
Then
Version 2
The second version of the Fundamental Theorem of Calculus states that
This last formula can also be expressed in terms of an indefinite integral:
where C is a constant.
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