# HW8 - ± t = ± ± ± ± I t-I a I t ± ± ± ± × 100...

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EMAE 250: Homework 8 March 22, 2011 1. Evaluate the following integral Z 6 0 ( - 2 + x - 3 x 2 + 4 x 4 - x 5 ) dx (a) [1pt] Analytically. (b) [1pt] Simpson’s 1/3 rule where n = 2; (c) [1pt] Simpson’s 1/3 rule where n = 6; (d) [1pt] Simpson’s 3/8 rule where n = 3; (e) [1pt] Simpson’s 3/8 rule where n = 6, where n is the number of segments. (f) [2pt] Compute the true percent relative error for each (b) - (e) based on the analytical result from (a):
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Unformatted text preview: ± t = ± ± ± ± I t-I a I t ± ± ± ± × 100% where I t is the true value and I a is an estimated integral. 2. [3pt] Use the Romberg integration algorithm to evaluate Z 2 e 2 x sin( x ) 1 + x 2 dx to the error equal or smaller than 0.5%. Use an estimate of the percent relative error deﬁned by ± a = ± ± ± ± ± I 1 ,k-I 2 ,k-1 I 1 ,k ± ± ± ± ± × 100% . 1...
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