Unformatted text preview: requires an even number of intervals, but we don’t know how many are required to obtain the desired threeplace accuracy. Rather than make an error analysis, we will compute the approximate value of y (0 . 5) using 2, 4, 6, . . . intervals for Simpson’s rule until the approximate values for y (0 . 5) change by less than ±ve in the fourth place. ²or n = 2, we divide [0 , . 5] into 4 equal subintervals. Thus each interval will be of length (0 . 5 − 0) / 4 = 1 / 8 = 0 . 125. Therefore, the integral is approximated by . 5 Z e x 2 dx = 1 24 h e + 4 e (0 . 125) 2 + 2 e (0 . 25) 2 + 4 e (0 . 325) 2 + e (0 . 5) 2 i ≈ . 544999003 . 32...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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