This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: THE DEFINITE INTEGRAL We saw a limit of the form lim n [ f ( x * 1 ) x + f ( x * 2 ) x + + f ( x * n ) x ] = lim n n X i =1 f ( x * i ) x Because this form arises frequently in a wide variety of situations, we give this type of limit a special name and notation. Definition 1. If f is a continuous function defined for a x b , we divide the interval [ a,b ] into n subintervals of equal width x = ( b a ) /n . We let x = a,x 1 ,x 2 , ,x n = b be the endpoints of these subintervals and we let x * 1 ,x * 2 , ,x * n be any sample points in these subintervals, so x * i lies in the i th subinterval [ x i 1 ,x i ]. Then, the definite integral of f from a to b is Z b a f ( x ) dx = lim n n X i =1 f ( x * i ) x The symbol R is called an integral sign . In the notation Z b a f ( x ) dx , f ( x ) is called the integrand and a and b are called the limits of integration; a is the lower limit and b is the upper limit . The procedure of calculating an integral is called....
View
Full
Document
This note was uploaded on 03/27/2012 for the course MATH 1a taught by Professor Benedictgross during the Fall '09 term at Harvard.
 Fall '09
 BenedictGross

Click to edit the document details