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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?...
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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.
 Spring '08
 ALL
 Calculus, Geometry

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