From dc700de66e1922dd1f38a9e8e5069285ec4a7a47 Mon Sep 17 00:00:00 2001 From: arc Date: Sun, 6 Apr 2025 12:18:45 -0600 Subject: [PATCH] vault backup: 2025-04-06 12:18:45 --- education/math/MATH1210 (calc 1)/Integrals.md | 1 + 1 file changed, 1 insertion(+) diff --git a/education/math/MATH1210 (calc 1)/Integrals.md b/education/math/MATH1210 (calc 1)/Integrals.md index a071c65..8479dbe 100644 --- a/education/math/MATH1210 (calc 1)/Integrals.md +++ b/education/math/MATH1210 (calc 1)/Integrals.md @@ -88,6 +88,7 @@ Average = $\dfrac{1}{b-a} \int_a^b f(x)dx$ $$\int_a^b f(x) dx = F(b) - F(a)$$ 2. Let $f$ be a continuous function on $[a, b]$ and let $x$ be a point in $[a, b]$. $$ F(x) = \int_a^x f(t)dt \Rightarrow F'(x) = f(x) $$ +This basically says that cancelling out the derivative from $a$ to $x$ can be done by $$ \dfrac{d}{dx} \int_a^{g(x)} f(t) dt = f(g(x)) * g'(x)* $$ ## Examples > Finding the derivative of an integral