From 49918dcd5df90a5754104002f935026ff097d289 Mon Sep 17 00:00:00 2001 From: arc Date: Thu, 27 Mar 2025 09:26:27 -0600 Subject: [PATCH] vault backup: 2025-03-27 09:26:27 --- education/math/MATH1210 (calc 1)/Integrals.md | 9 ++++++++- 1 file changed, 8 insertions(+), 1 deletion(-) diff --git a/education/math/MATH1210 (calc 1)/Integrals.md b/education/math/MATH1210 (calc 1)/Integrals.md index 4110345..dfef23d 100644 --- a/education/math/MATH1210 (calc 1)/Integrals.md +++ b/education/math/MATH1210 (calc 1)/Integrals.md @@ -69,4 +69,11 @@ $$ \Delta x = \dfrac{1 - 0}{n} = \dfrac{1}{n}$$$$ x_i = 0 + \Delta xi + \dfrac{1 4. $= \lim_{n \to \infty} \dfrac{5}{n^2} \sum_{i = 1}^n i$ 5. $= \lim_{x \to \infty} \dfrac{5}{n^2} \cdot \dfrac{n(n + 1)}{2}$ 6. $= \lim_{n \to \infty} \dfrac{5n^2 + 5n}{2n^2}$ -7. $= \dfrac{5}{2}$ \ No newline at end of file +7. $= \dfrac{5}{2}$ + +# Properties of Integrals +1. $\int_a^a f(x)dx = 0$ +2. $\int_b^a f(x)dx = -\int_a^b f(x) dx$ +3. $\int_a^b cf(x) dx = c \int_a^b f(x) dx$ +4. $\int_a^b f(x) \pm g(x) dx = \int_a^b f(x) dx \pm \int_a^b g(x)dx$ +5. $\int \ No newline at end of file