864 B
864 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
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R=[a,b] \times [c,d] - x values are between
aandb, y values are betweencandd
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- slice up solid into equations that can be integrated with one variable
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\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
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\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)
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