Stewart6e5_2part2

# Stewart6e5_2part2 - MATH 191 Sections 1 and 3 Calculus I...

This preview shows pages 1–2. Sign up to view the full content.

Calculus I Fall 2007 Section 5.2, part II: More on Deﬁnite Integrals Recall that R b a f ( x ) dx = lim n →∞ n X i =1 f ( x * i x , where x * i is a sample point chosen from the subinterval [ x i - 1 , x i ]. Our computations using Mathematica have shown us that in selecting x * i to be the midpoint x i = x i - 1 + x i 2 of the interval [ x i - 1 , x i ], we obtain a better estimate than if we use either endpoint. This is the basis of the so-called Midpoint Rule. R b a f ( x ) dx n X i =1 f ( x i x . Very often this estimate is good enough for whatever purpose it’s needed. Example. Use the Midpoint Rule with n = 4 to estimate the integral R 3 1 1 x dx . How far oﬀ are we, according to Mathematica ? Before we move on, we should point out a number of properties of the deﬁnite integral, most of which follow from basic computations and the deﬁnition of the integral. In the properties below, let c be any constant, and let f and g both be integrable on the interval [

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

Stewart6e5_2part2 - MATH 191 Sections 1 and 3 Calculus I...

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

View Full Document
Ask a homework question - tutors are online