From 56f0fa193b2280dd0b2a040da9b4f792ba2b9a95 Mon Sep 17 00:00:00 2001 From: arc Date: Tue, 1 Apr 2025 09:53:23 -0600 Subject: [PATCH] vault backup: 2025-04-01 09:53:23 --- 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 98360d3..c2827d5 100644 --- a/education/math/MATH1210 (calc 1)/Integrals.md +++ b/education/math/MATH1210 (calc 1)/Integrals.md @@ -87,4 +87,6 @@ Average = $\dfrac{1}{b-a} \int_a^b f(x)dx$ 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 +$$ F(x) = \int_a^x f(t)dt \Rightarrow F'(x) = f(x) $$ +$$ \dfrac{d}{dx} \int_a^{g(x)} f(t) dt = f(g(x)) * g'(x)* $$ +$$ \dfrac{d}{dx} \int_2^{7x} \cos(t^2) dt = $$ \ No newline at end of file