MATH 140 Lecture Notes - Lecture 28: Riemann Sum, If And Only If

• School: University of Maryland
• Department: Mathematics
• Course: MATH 140
• Professor: Gulick

Document Summary

A smaller< a larger o o o: lower and upper sums: U f ( p)= m1(x1 x0)+ m n(xn xn 1) o o: note: lf ( p) u f (p, partitions, let p be a partition by adding points to p; p is a refinement of p. Lf ( p) lf ( p ) u f ( p ) u f (p) o: result: let f be continuous on [a, b], and let p and q be partitions of [a, b]. Lf ( p) u f (q: let p be a common refinement of p and q. Lf ( p) lf ( p ) u f ( p ) u f (q: if f 0 on [a, b] then the area of the region below the graph of f and above the x axis on [a, b] is a. Note that lf ( p) a u f (p)