From 3ce3b8a446e392cbf92cdebcaeda3c02b020ea4a Mon Sep 17 00:00:00 2001 From: arc Date: Thu, 27 Mar 2025 09:41:27 -0600 Subject: [PATCH] vault backup: 2025-03-27 09:41:27 --- education/math/MATH1210 (calc 1)/Integrals.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/education/math/MATH1210 (calc 1)/Integrals.md b/education/math/MATH1210 (calc 1)/Integrals.md index 8ac7fb1..6f2c40f 100644 --- a/education/math/MATH1210 (calc 1)/Integrals.md +++ b/education/math/MATH1210 (calc 1)/Integrals.md @@ -81,4 +81,8 @@ $$ \Delta x = \dfrac{1 - 0}{n} = \dfrac{1}{n}$$$$ x_i = 0 + \Delta xi + \dfrac{1 # Averages To find the average value of $f(x)$ on the interval $[a, b]$ is given by the formula: -Average = $\dfrac{1}{b-a} \int_a^b f(x)dx$ \ No newline at end of file +Average = $\dfrac{1}{b-a} \int_a^b f(x)dx$ + +# The Fundamental Theorem of Calculus +Let $f$ be a continuous function on the closed interval $[a, b]$ and let $F$ be any antiderivative of $f$, then: +$$\int_a^b f(x) dx = F(b) - F(a)$$