From 7d7562e27c3fb1fc1ed54ea59fe670396bfd3be7 Mon Sep 17 00:00:00 2001 From: arc Date: Tue, 1 Apr 2025 09:43:23 -0600 Subject: [PATCH] vault backup: 2025-04-01 09:43:23 --- education/math/MATH1210 (calc 1)/Integrals.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/education/math/MATH1210 (calc 1)/Integrals.md b/education/math/MATH1210 (calc 1)/Integrals.md index 6f2c40f..98360d3 100644 --- a/education/math/MATH1210 (calc 1)/Integrals.md +++ b/education/math/MATH1210 (calc 1)/Integrals.md @@ -84,5 +84,7 @@ To find the average value of $f(x)$ on the interval $[a, b]$ is given by the for Average = $\dfrac{1}{b-a} \int_a^b f(x)dx$ # The Fundamental Theorem of Calculus -Let $f$ be a continuous function on the closed interval $[a, b]$ and let $F$ be any antiderivative of $f$, then: +1. Let $f$ be a continuous function on the closed interval $[a, b]$ and let $F$ be any antiderivative of $f$, then: $$\int_a^b f(x) dx = F(b) - F(a)$$ +2. Let $f$ be a continuous function on $[a, b]$ and let $x$ be a point in $[a, b]$. +$$ F(x) = \int_a^x f(t)dt \Rightarrow F'(x) = f(x) $$ \ No newline at end of file