5.1 Estimating the Finite Sum

# 5.1 Estimating the Finite Sum - 1 5.1 Estimating with...

This preview shows pages 1–3. Sign up to view the full content.

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.

Unformatted text preview: 1 5.1 Estimating with Finite Sums There is no easy formula for finding the area of a region bounded by a curve. Our goal for today is to develop a method for approximating the area by covering the region with a collection of rectangles. Consider a region bounded by a graph of a function f ( x ) a b x y f H x L We can estimate the area under the graph by adding the areas of the approx- imating rectangles. However, we must decide how tall our rectangles must be. Area ≈ Where Δ x = , and n is a number of subintervals. The long summation can be written in short form using sigma notation: Area ≈ The sums of this form are called 2 The approximation is determined by how you choose the height of each rect- angle. Definition S L : Left-endpoint Riemann Sum Choose the height of each rectangle on the interval [ x i ,x i +1 ]to be a b x y f H x L Area ≈ S R : Right-endpoint Riemann Sum Choose the height of each rectangle on the interval [ x i ,x i +1 ]to be a b x y f H x L Area ≈ S M : Midpoint...
View Full Document

## This note was uploaded on 10/02/2011 for the course MATH 1206 taught by Professor Llhanks during the Fall '08 term at Virginia Tech.

### Page1 / 5

5.1 Estimating the Finite Sum - 1 5.1 Estimating with...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online