vault backup: 2025-08-26 12:41:25
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@ -7,7 +7,7 @@ Let $x_0, x_1, x_2, \cdots, x_n$ be the endpoints of this subdivision. $x_0 = a$
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Define $$\int_a^b f(x) dx = \lim_{n \to \infty} \sum_{i=1}^nf(x_i)\Delta x$$
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- $\Delta x$ refers to the width of each sub-interval
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- $f(x_i)$ refers to the height of each subinterval.
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- $f(x_i)$ refers to the height of each subinterval, and can be found with the equation $x_i = \Delta xi + a$
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Then let $f$ be a continous function on $[a, b]$ and let $F$ be the antiderivative of $f$ (i.e $F'(x) = f(x)$).
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Then $\int_a^b f(x) dx = F(b) - F(a)$.
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