vault backup: 2025-04-01 09:43:23
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@ -84,5 +84,7 @@ To find the average value of $f(x)$ on the interval $[a, b]$ is given by the for
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Average = $\dfrac{1}{b-a} \int_a^b f(x)dx$
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# The Fundamental Theorem of Calculus
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Let $f$ be a continuous function on the closed interval $[a, b]$ and let $F$ be any antiderivative of $f$, then:
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1. Let $f$ be a continuous function on the closed interval $[a, b]$ and let $F$ be any antiderivative of $f$, then:
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$$\int_a^b f(x) dx = F(b) - F(a)$$
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2. Let $f$ be a continuous function on $[a, b]$ and let $x$ be a point in $[a, b]$.
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$$ F(x) = \int_a^x f(t)dt \Rightarrow F'(x) = f(x) $$
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