For equation: 1 = (60 = (ex + cos x) dx a. Calculate the...

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For equation: 1 = √ (6²0 = √ (e²x + cos x) dx a. Calculate the integral using Simpson 3/8. b. Calculate the integral using Romberg with n=3 steps. You will need trapezoid integration up to 8 segments (j=4). c. Calculate the integral using Gauss-Quadrature with 3 points. d. Calculate the error percentage of each part using exact solution. Comment on results, which method provides the best result, which one requires the most calculations and etc. The exact result from analytic solution is 264.63345 For equation: 1 = √ (6²0 = √ (e²x + cos x) dx a. Calculate the integral using Simpson 3/8. b. Calculate the integral using Romberg with n=3 steps. You will need trapezoid integration up to 8 segments (j=4). c. Calculate the integral using Gauss-Quadrature with 3 points. d. Calculate the error percentage of each part using exact solution. Comment on results, which method provides the best result, which one requires the most calculations and etc. The exact result from analytic solution is 264.63345

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To calculate the integral using different methods and evaluate their errors well need to define the integrand function and perform the calculations step by step Lets start with the Simpson 38 rule a S... View the full answer