{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Definite integral

Definite integral - THE DEFINITE INTEGRAL We saw a limit of...

Info iconThis preview shows pages 1–2. 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 Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: THE DEFINITE INTEGRAL We saw a limit of the form lim n →∞ [ f ( x * 1 )Δ x + f ( x * 2 )Δ x + ··· + f ( x * n )Δ x ] = lim n →∞ n X i =1 f ( x * i )Δ 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 Δ 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 )Δ 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

{[ snackBarMessage ]}

Page1 / 3

Definite integral - THE DEFINITE INTEGRAL We saw a limit of...

This preview shows document pages 1 - 2. Sign up to view the full document.

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