From 5734922daef426c4fa0a949db74be4dbb0c086fe Mon Sep 17 00:00:00 2001 From: arc Date: Mon, 25 Aug 2025 12:19:25 -0600 Subject: [PATCH] vault backup: 2025-08-25 12:19:25 --- education/math/MATH1220 (calc II)/Integral Review.md | 12 ++++++++++++ 1 file changed, 12 insertions(+) create mode 100644 education/math/MATH1220 (calc II)/Integral Review.md diff --git a/education/math/MATH1220 (calc II)/Integral Review.md b/education/math/MATH1220 (calc II)/Integral Review.md new file mode 100644 index 0000000..1e67d3f --- /dev/null +++ b/education/math/MATH1220 (calc II)/Integral Review.md @@ -0,0 +1,12 @@ +# Formal Definition +Let $f$ be a continuous function on an interval $[a, b]$. + +Divide $[a, b]$ into $n$ equal parts of width $\Delta x = \dfrac{b-a}{n}$. + +Let $x_0, x_1, x_2, \cdots, x_n$ be the endpoints of this subdivision. $x_0 = a$ and $x_n = b$. + +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 +- $f(x_i)$ refers to the height of each subinterval. + +Then let $f$ be a continous function on $[a, b]$ and let $F$ be the any derivative of $f$ (i.e ) \ No newline at end of file