Consider the following integral: ex sin(x) I = dx 1+x 0 1. Compute the integral 11/3...

   

 

 

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Consider the following integral: ex sin(x) I = dx 1+x 0 1. Compute the integral 11/3 using a single application of Simpson's 1/3 rule 2. Compute the integral 13/8 using a single application of Simpson's 3/8 rule 3. Determine the percentage error between the two results. i.e. error % = 11-13 13 8 8 100% 4. Repeat steps 1-3 with an added application to each rule until the percentage error is less than 1e-5%. Use fprintf to print the number of applications required to achieve a percentage error less than 1e-5% between the two rules. In addition, print the corresponding number of points needed for each rule. Consider the following integral: ex sin(x) I = dx 1+x 0 1. Compute the integral 11/3 using a single application of Simpson's 1/3 rule 2. Compute the integral 13/8 using a single application of Simpson's 3/8 rule 3. Determine the percentage error between the two results. i.e. error % = 11-13 13 8 8 100% 4. Repeat steps 1-3 with an added application to each rule until the percentage error is less than 1e-5%. Use fprintf to print the number of applications required to achieve a percentage error less than 1e-5% between the two rules. In addition, print the corresponding number of points needed for each rule.