From ee8ce9ca14840317659a813b6f4df5871c71ba86 Mon Sep 17 00:00:00 2001 From: arc Date: Wed, 27 Aug 2025 11:44:05 -0600 Subject: [PATCH] vault backup: 2025-08-27 11:44:05 --- education/math/MATH1220 (calc II)/Integration by Parts.md | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/education/math/MATH1220 (calc II)/Integration by Parts.md b/education/math/MATH1220 (calc II)/Integration by Parts.md index 319ca0e..ae79efb 100644 --- a/education/math/MATH1220 (calc II)/Integration by Parts.md +++ b/education/math/MATH1220 (calc II)/Integration by Parts.md @@ -5,6 +5,7 @@ $$ \int udv = uv - \int vdu $$ $$ \frac{d}{dx}(f(x)g(x)) = f'(x)g(x) + f(x)g'(x) $$ 1. Integrating both sides, we get: $$\int \frac{d}{dx} (f(x)g(x))dx = \int [f'(x)g(x) + f(x)]$$ - -2. Therefore: -$$$$ \ No newline at end of file +2. Through the distributive property of integrals, +$$ = \int f'(x)g(x)dx + \int f(x)g'(x)dx $$ +3. Therefore: +$$f(x)g(x) = \intf'(x)g(x)dx $$ \ No newline at end of file