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College/AU 26/MATH 224 (Multivar)/Class 10-5.md

@@ -1,3 +1,14 @@
 #uw/notes #uw/class/math224 
 - - -
-- 
+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 
+$$\begin{gathered} 1<x<2 \\[1.5ex] x < y < x^2 \end{gathered}$$