{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lab1_approximation_errors

# lab1_approximation_errors - Math 172 Integral Calculus Prof...

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

Math 172: Integral Calculus Prof. Thomas Pietraho Fall, 2007 Lab 1: Approximation Errors Part 1 1 Motivation Many functions do not have an elementary antiderivative, and to evaluate a definite integral of such a function, we will need to resort to methods of approximation. The goal of this lab is to examine the approximation of a definite integral using its Riemann sums. Let’s first examine the integral S = Z π 0 e - x 2 dx. We are most interested in finding out the effect of increasing the number of intervals used in the sum has on the accuracy of the approximation. 2 Left Riemann Sums Let’s first get some data for the integral above. Mathematica can find the value of S exactly, and using the Joy of Mathematica menus, it is possible to find the left Riemann sums for different numbers of intervals. 1. For starters, first determine the numerical value of S using Mathematica . 2. Let’s use the left end point method to estimate S using 2, 4, 8, 16, 32, 64, and 128 subintervals. Joy facilitates this computation through the

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 ]}