5.2 The Definite Integral

Mathematica script by Chris Parrish,

cparrish@sewanee.edu

Sources and references for some of these problems include

James Stewart, "Calculus: Concepts and Contexts," Second Edition, Brooks/Cole, 2001

Deborah Hughes-Hallett, Andrew M. Gleason, et. al., "Calculus," Second Edition, John Wiley & Sons, 1998

Robert Fraga, ed., "Calculus Problems for a New Century," The Mathematical Association of America, 1993

Code for the Mathematica procedures AreaR, AreaL, and AreaM is modified slightly from programs developed in

Finch and Lehmann, "Exploring Calculus with Mathematica," Addison-Wesley, 1992

AreaR, AreaL, AreaM -- contains Mathematica code only, not worked exercises

Using Rectangles to Estimate the Area of the Region

under the Graph of f(x) = 2 - and over the interval [0,2].

Stewart, Exercise 5.2.1, page 367

Using Rectangles to Estimate the Area of the Region

under the Graph of f(x) = ln x - 1 and over the interval [1,4].

Stewart, Exercise 5.2.1, page 367

Clear[f,x];

f[x_] := Log[x] - 1;

a = 1; (* a = lefthand endpoint *)

b = 4; (* b = righthand endpoint *)

n = 6; (* n = number of rectangles *)

AreaLVerbose[f,a,b,n];

Using Rectangles to Estimate the Area of the Region

under the Graph of f(x) = and over the interval [0,2].

Stewart, Exercise 5.2.16, page 368

Created by Mathematica (April 6, 2004)