MATH 140 Lecture 29: Integral Properties

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

Document Summary

U f ( p)=f (c) h+f (c+h)h+f (c+2h)h+ +f ( c+(n 1)h) h. Lf ( p)=f (c+h) h+f (c +2h) h+ f ( c+h)h o o o: properties of area: A small< alarge o o o: riemann sums, upper sum, lower sum, left sum, right sum, midpoint sum. F (x ) dx =a b a: remember that lf ( p) b a f ( x) dx u f (p) for any partition p. Important properties of integrals a a f (x)dx=0: let a c b , then b a f ( x) dx= f (x)dx + f ( x)dx c a b c b a a b f (x)dx= f ( x) dx= . Then, b a f ( x)+g(x )d= f (x)dx+ g (x)dx b a a b b a: some simple integrals: b a b a b a. Dx= (b a) c dx=c (b a) cx dx= c.