L24 Math 233 Lecture Notes - Lecture 25: Riemann Sum, Nissan L Engine, Iterated Integral
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L24 math 233 lecture 25- integration for functions of two variables. Integral of f(x) = area under the graph. This area can be approximated with rectangles using the riemann sum n (x )( x ) [xn 1 xn and using as the subinterval which will have width. For definiteness, we may assume that subintervals are equally wide by putting xn = a + n. Definition: f is integrable on [a,b] is any choices x* Theorem: if f(x) is continuous on [a,b], then f is integrable. Idea: find the upper and lower sums (x )( x ) n n=1 lim n . *n f exists and is the same for every x n = n. )( x ) n where max xn is the point in the domain where f. )( x ) n where min xn is the point in the domain where f (f, (f, lim n .
