#uw/notes #uw/class/math224
- - -
- definite integral represents the signed area between a function and the x axis between the two bounds
	- $\int_{a}^b f(x) dx$
	- for functions with one variable
	- riemann sums: $$\int_{a}^b f(x) dx = \lim_{ n \to \infty } f(x^*_{k}) \Delta x$$
- double integral
	- $f(x,y)$
	- $$\int \int_{R} f(x,y) dA$$
	- represents the signed volume between the xy plane and the graph of $z=f(x,y)$ above the region $R$
	- defining region
		- $$R=[a,b] \times [c,d]$$
		- 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
	- $$\int \int_{[a,b] \times [c,d]} f(x,y) dA = \int^b_{a} \int^d_{c}f(x,y)dy dx$$
	-