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Unformatted text preview: Assignment #6: Numerical Integration (part 1) Due date: Wednesday, October 27, 2010 (10:15am) For full credit you must show all of your work. 1. The definite integral e x " 1 x 1 # dx = 1.3179 (to five decimal digits of accuracy). Show how one could estimate e x " 1 x 1 # dx without using numerical integration (hint: you will want to use an alternative strategy discussed near the beginning of the semester). 2. The concepts of upper and lower sums provide a theoretical foundation for the process of numerical integration. By hand, show how to use the method of Lower Sums to estimate the following definite integrals using the specified partitions: a. [2 cos( x + " 2 ) # 3] dx " $ , with partition P a = {0, π /2, π } b. [2 cos( x + " 2 ) # 3] dx " 2 " $ , with partition P b = { π , 3 π /2, 2 π } Repeat using upper sums, with the same partitions. Analytically determine the exact solutions to each of these definite integrals. Which of your two estimates (obtained using upper sums or lower sums) is closer to the exact solution in each case? Do you notice anything about the shape of the function over each of the intervals that could predict when the upper vs. lower sum will be closer to the actual solution?...
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This note was uploaded on 11/29/2010 for the course CSCI cs taught by Professor Intern during the Fall '10 term at Minnesota.
 Fall '10
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