For the integral 2x I = 1-1² 1+x29x (a) (2m) Calculate I analytically. Solve by hand or using a symbolic solver such as the symbolic toolbox in MATLAB, Maple, or other symbolic math tool. (b) (2m) Plot f(x) (the integrand) for x = 0 to 5. (c) (2m) Calculate the integral numerically using the composite trapezoid method, using the number of subintervals n = 1 through 100. (d) (3m) Revise the composite Simpson 3/8 function to add header comments, add error check- ing of N into the beginning of the function, and return the revised value of N. (e) (1m) Calculate the integral numerically using the revised function for the composite Simp- son 3/8 method, using the number of subintervals N = 1 through 100. (f) (4m) Plot N versus I and N versus the error in I (use subplot) for both methods and discuss the plot. (g) (3m) Determine the value of N at which the numerical answer is within five significant digits of the analytical answer, use round().