Fundamental Theorem of Calculus
The fundamental theorem of calculus is used to calculate the antiderivative on an interval. There are two parts to the fundamental theorem of calculus.
Part 1:
The first part of the fundamental theorem of calculus is used for indefinite integrals and is the following.
This is basically a reverse differentiation where d/dx is equal to f(t). The antiderivative is continuous and can be differentiated on an open interval. To get the antiderivative you must evaluate doing F(b)-F(a). The capital F being the antiderivative.
Here are some example problems using the first part of the fundamental theorem of calculus.
Here are some example problems using the first part of the fundamental theorem of calculus.
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Part 2:
The second part of the fundamental theorem of calculus is similar to the first, except we are solving for the exact antiderivative whcih will give us a constant. This can be used to represent the area under a curve.