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education/math/MATH1220 (calc II)/Integral Review.md
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@ -7,7 +7,7 @@ Let $x_0, x_1, x_2, \cdots, x_n$ be the endpoints of this subdivision. $x_0 = a$
Define $$\int_a^b f(x) dx = \lim_{n \to \infty} \sum_{i=1}^nf(x_i)\Delta x$$ Define $$\int_a^b f(x) dx = \lim_{n \to \infty} \sum_{i=1}^nf(x_i)\Delta x$$
- $\Delta x$ refers to the width of each sub-interval - $\Delta x$ refers to the width of each sub-interval
- $f(x_i)$ refers to the height of each subinterval. - $f(x_i)$ refers to the height of each subinterval, and can be found with the equation $x_i = \Delta xi + a$
Then let $f$ be a continous function on $[a, b]$ and let $F$ be the antiderivative of $f$ (i.e $F'(x) = f(x)$). Then let $f$ be a continous function on $[a, b]$ and let $F$ be the antiderivative of $f$ (i.e $F'(x) = f(x)$).
Then $\int_a^b f(x) dx = F(b) - F(a)$. Then $\int_a^b f(x) dx = F(b) - F(a)$.