From f53a551f7b3fba1a825fbba4be3faf40a0195113 Mon Sep 17 00:00:00 2001 From: arc Date: Mon, 25 Aug 2025 13:18:14 -0600 Subject: [PATCH] vault backup: 2025-08-25 13:18:14 --- education/math/MATH1220 (calc II)/Integral Review.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/education/math/MATH1220 (calc II)/Integral Review.md b/education/math/MATH1220 (calc II)/Integral Review.md index 1e67d3f..ce78244 100644 --- a/education/math/MATH1220 (calc II)/Integral Review.md +++ b/education/math/MATH1220 (calc II)/Integral Review.md @@ -9,4 +9,8 @@ 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 +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 $\int_a^b f(x) dx = F(b) - F(a)$. + +## Examples +$$ \int_0^1 x^2 dx = \frac{1}{3} x^3 \Big |_0^1 = 1/3(1^3)- 1/3 (0)^3 = 1/3$$ \ No newline at end of file