Question: 2 Comparisons of numerical integration methods (80 points) Compute the following integration. 014x3ex4dx Use 3 different methods, including (1) adaptive Simpson's rule, (2) Romberg's method

2 Comparisons of numerical integration methods (80 points) Compute the following

2 Comparisons of numerical integration methods (80 points) Compute the following integration. 014x3ex4dx Use 3 different methods, including (1) adaptive Simpson's rule, (2) Romberg's method and (3) Gaussian quadrature. Compare with the analytical results to plot the errors versus the number of intervals N in a log-log plot. Use the following values of N for all 3 methods, (4,8,16,32,64,128). (Use gaussxw . py in the folder for lecture 6 on Canvas to calculate the weights and integration points for Gauss quadrature.)

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