From f8ada83366f349ac148e4d9407b9b9f2ee31dd76 Mon Sep 17 00:00:00 2001 From: arc Date: Wed, 27 Aug 2025 11:39:05 -0600 Subject: [PATCH] vault backup: 2025-08-27 11:39:05 --- education/math/MATH1210 (calc 1)/Derivatives.md | 2 +- .../math/MATH1220 (calc II)/Integration by Parts.md | 10 ++++++++++ 2 files changed, 11 insertions(+), 1 deletion(-) create mode 100644 education/math/MATH1220 (calc II)/Integration by Parts.md diff --git a/education/math/MATH1210 (calc 1)/Derivatives.md b/education/math/MATH1210 (calc 1)/Derivatives.md index 1ef3a4e..f764cc6 100644 --- a/education/math/MATH1210 (calc 1)/Derivatives.md +++ b/education/math/MATH1210 (calc 1)/Derivatives.md @@ -1,4 +1,4 @@ -SA derivative can be used to describe the rate of change at a single point, or the *instantaneous velocity*. +A derivative can be used to describe the rate of change at a single point, or the *instantaneous velocity*. The formula used to calculate the average rate of change looks like this: $$ \dfrac{f(b) - f(a)}{b - a} $$ diff --git a/education/math/MATH1220 (calc II)/Integration by Parts.md b/education/math/MATH1220 (calc II)/Integration by Parts.md new file mode 100644 index 0000000..319ca0e --- /dev/null +++ b/education/math/MATH1220 (calc II)/Integration by Parts.md @@ -0,0 +1,10 @@ +The integration by parts formula is: +$$ \int udv = uv - \int vdu $$ + +## Deriving the Integration by Parts Formula +$$ \frac{d}{dx}(f(x)g(x)) = f'(x)g(x) + f(x)g'(x) $$ +1. Integrating both sides, we get: +$$\int \frac{d}{dx} (f(x)g(x))dx = \int [f'(x)g(x) + f(x)]$$ + +2. Therefore: +$$$$ \ No newline at end of file