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lab1_approximation_errors - Math 172 Integral Calculus Prof...

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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
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