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vault backup: 2026-10-03 15:29:15

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College/AU 26/MATH 224 (Multivar)/Class 10-2.md
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@@ -13,4 +13,6 @@
- x values are between $a$ and $b$ , y values are between $c$ and $d$ - x values are between $a$ and $b$ , y values are between $c$ and $d$
- slice up solid into equations that can be integrated with one variable - slice up solid into equations that can be integrated with one variable
- $$\int \int_{[a,b] \times [c,d]} f(x,y) dA = \int^b_{a} \int^d_{c}f(x,y)dy dx$$ - $$\int \int_{[a,b] \times [c,d]} f(x,y) dA = \int^b_{a} \int^d_{c}f(x,y)dy dx$$
- - Fubini's theorem
- $$\int_{a}^b \int_{c}^d f(x,y) dy dx = \int_{c}^d \int_{a}^b f(x,y) dx dy$$
- can integrate either way (x or y first)