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# hw7 - Assignment#7 Numerical Integration(part 2 Due date...

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Assignment #7: Numerical Integration (part 2) Due date: Wednesday, November 3, 2010 (10:15am) For full credit you must show all of your work. 1. Estimate e cos2 x dx 0 " # using Basic Simpson’s rule. If the actual solution, to within 5 decimal places of accuracy, is 3.97746, what is the absolute error in the approximate answer you obtain? What is the error term for this approximation? If –92 < d 4 dx 4 e cos2 x ( ) < 174 for 0 x π , what is the upper bound on the error that you get by using this formula? What can you conclude from this about the practicality of using the upper bound on the error in the Basic Simpson’s rule to estimate the actual amount of error that will occur when applying it? 2. Using Matlab, write a program that implements the composite Simpson’s rule . Structure your code so that it can be easily re-used to estimate a variety of different definite integrals. a. Test your program by using it to estimate sin( x ) dx 0 " # . If the true solution is 2, at how many points do you need to evaluate the function to obtain an estimate that is accurate to within 5 decimal places ( ε ½ × 10 –5 ), and what is the distance between neighboring points?

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hw7 - Assignment#7 Numerical Integration(part 2 Due date...

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