hw8_solutionsMAE107

# hw8_solutionsMAE107 - Homework 8 solution 17.4(a Analytical...

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Homework 8 solution 17.4- (a)  Analytical integration yields: 2 4 1 x 4x 3 2x 5 dx =[ x x 2 2 x 4 x 6 3 ] 2 4 = 1104          (b)  Single application of the Trapezoidal rule gives:   4 −− 2  29 1789 2 = 5280           (c)  Composite Trapezoidal rule with  n=2  : 4 −− 2  29 2 − 2  1789 4 = 2634 Composite Trapezoidal rule with  n=4  : 4 −− 2  29 2 1.9375 − 2  131.3125  1789 8 = 1516.875   (d)  Single Simpson's 1/3 rule gives:   4 −− 2  29 4 − 2  1789 6 = 1752    (e)  Composite Simpson's 1/3 rule with  n=4  gives: 4 −− 2  29 4 1.9375 131.3125  2 − 2  1789 12 = 1144.5                (f)   And finally, Simpson's 3/8 rule gives: 4 −− 2  29 3 1 31  1789 8 = 1392

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The percent relative errors calculated based on the analytical solution are:
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