lecture32a - Lecture 32 (Chapter 5, Sec. 32): The Definite...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture 32 (Chapter 5, Sec. 32): The Definite Integral Def. If f is defined for a x b , divide [ a,b ] into n subintervals of equal width x = Let x (= a ) ,x 1 ,x 2 ,...,x n (= b ) be the endpoints of these subintervals and let x * i be any sample point in the subinterval [ x i- 1 ,x i ]. The definite integral of f from a to b is if the limit exists. If so, f is integrable on [ a,b ]. The sum n X i =1 f ( x * i ) x is a It is used to approximate the definite integral. 2 Notation Integral sign Integrand Integration Limits of integration (lower and upper) dx NOTE: Theorem: If f is continuous or has a finite number of jump discontinuities on [ a,b ], then f is integrable on [ a,b ]. 3 ex. Express lim n n X i =1 x * i e ( x * i ) 2- 3 x as a definite integral on [0 , 4]. Riemann Sums, Definite Integral, and Area: If f ( x ) 0 on [ a,b ] 6- ? If f ( x ) 0 for some x in [ a,b ] 6- ? 4 How to evaluate definite integrals?...
View Full Document

This note was uploaded on 05/17/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

Page1 / 12

lecture32a - Lecture 32 (Chapter 5, Sec. 32): The Definite...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online