724 B
724 B
#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 regionR - defining region
-
R=[a,b] \times [c,d] - x values are between
aandb, y values are betweencandd
-
- 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