From 3bbe98fa13f8bc87b280c54c435496ce010f54e1 Mon Sep 17 00:00:00 2001 From: ben-jaynes <1btjaynes@gmail.com> Date: Mon, 5 Oct 2026 11:44:07 -0700 Subject: [PATCH] vault backup: 2026-10-05 11:44:07 --- College/AU 26/MATH 224 (Multivar)/Class 10-5.md | 13 ++++++++++++- 1 file changed, 12 insertions(+), 1 deletion(-) diff --git a/College/AU 26/MATH 224 (Multivar)/Class 10-5.md b/College/AU 26/MATH 224 (Multivar)/Class 10-5.md index 888447c..9b01809 100644 --- a/College/AU 26/MATH 224 (Multivar)/Class 10-5.md +++ b/College/AU 26/MATH 224 (Multivar)/Class 10-5.md @@ -1,3 +1,14 @@ #uw/notes #uw/class/math224 - - - -- \ No newline at end of file +Recall that: +$$\int \int_{R} f(x, y) dA$$ +is the signed area under the function $f(x,y)$ over the domain $R$ where +$$R=[a,b] \times [c,d]$$ +and it can be written as +$$\int_{a}^b \int_{c}^d f(x, y) dy dx$$ + +This can be extended to more general domains that are not rectangles such as $[a,b] \times [c,d]$ + +Example: +finding the volume under the function $f(x,y) = xy$ over the domain bound by +$$\begin{gathered} 1