Chapter 15.1 Double Integrals over Rectangles

December 2nd, 2024

Abdon Morales


Recall that: $\int_{a}^{b}{f(x) dx}$
Notice! The first step is to partition the domain.
Fubini's Theorem
If $f(x,y)$ is continous throughout the rectangular region $R = [a,b] \times [c,d]$ then:
$\begin{align} \iint_{R}{f(x,y) dA} &= \int_{c}^{d}{(\int_{a}^{b}{f(x,y) dx}) dy} \\ &\equiv \int_{a}^{b}{(\int_{c}^{d}{f(x,y) dy}) dx} \end{align}$
Example #1: $\iint_{R}{(20+xy) dA}$, let $R: 0\leq x\leq 3,\; -2\leq y\leq 2$
My way of solving this example:
$\begin{align} \end{align}$

$1+1=2$

Chapter 15.2 Double Integrals over General Regions

December 4th, 2024

Abdon Morales