MATH 140 Lecture Notes - Lecture 28: Riemann Sum

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

Document Summary

Recall: three properties of area, lower and upper sums: Then (cid:1838)(cid:3033)(cid:4666)(cid:1842)(cid:4667)(cid:3409)(cid:3033)(cid:4666)(cid:1843)(cid:4667): let (cid:1842) be a common refinement of p and q. Then (cid:1838)(cid:3033)(cid:4666)(cid:1842)(cid:4667)(cid:3409)(cid:1838)(cid:3033)(cid:4666)(cid:1842) (cid:4667)(cid:3409)(cid:3033)(cid:4666)(cid:1842) (cid:4667)(cid:3409) (cid:3033)(cid:4666)(cid:1843)(cid:4667): if (cid:1858)(cid:3410)(cid:882) 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 (cid:1838)(cid:3033)(cid:4666)(cid:1842)(cid:4667)(cid:3409)(cid:3409)(cid:3033)(cid:4666)(cid:1842)(cid:4667): note: if f (cid:882) throughout [a, b] then the statement is false, let f be continuous on [a, b] and let (cid:1842)={(cid:1853)=(cid:2868)