APFIVE Fundamental Theorem of Calculus Properties
All of the following statements about the Fundamental Theorem of Calculus (FTC) are true EXCEPT:
A
The FTC requires that an antiderivative used in evaluating $$\int_{a}^{b} f(x)\,dx$$ must be unique and not differ by a constant.
B
The FTC establishes a connection between differentiation and integration by showing that integration can be reversed by differentiation.
C
Any constant added to the antiderivative cancels out when computing $$F(b) - F(a)$$, so the constant of integration is not needed in definite integrals.
D
The FTC states that if $$F(x)$$ is an antiderivative of $$f(x)$$, then $$\int_{a}^{b} f(x)\,dx = F(b) - F(a)$$.
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