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The **Fundamental Theorem** of integral calculus states that if $g(x)$ is an antiderivative of a continuous $f(x)$, then $\int_a^b f(x)\,dx$ equals:
A$g(a) - g(b)$
B$g(b) - g(a)$
C$g(b) + g(a)$
D$g(b)/g(a)$
Answer & Solution
Correct answer: B. $g(b) - g(a)$
$\int_a^b f(x)\,dx = [g(x)]_a^b = g(b) - g(a)$. The constant of integration cancels in the subtraction.
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