Use python to create code that solves this problem. Simpsons Method is another approximation to the integral which uses parabolas instead of lines to approximate f(x): Z b a f(x) dx x/3(f(x0) + 2f(x1) + 4f(x2) + 2f(x3) + 4f(x4) + + 4f(xn2) + 2f(xn1) + f(xn)) (a) Use the function simps in the scipy.integrate package to compute Simpsons Approx- imation using n = 100 subintervals. (b) The value of the integral to 10 decimal places is 1.2112096245. Use this value to estimate the error |actual estimate| in each of the five approximations.

5. Simpson's Method is another approximation to the integral which uses parabolas instead of lines to approximate f(x): 12 - o) + 2f (21) + 4f(22) +2f(13) + 4f (14) + ... +4f (2n-2) + 2f (2n-1) + f(en)) 3 (a) Use the function simps in the scipy.integrate package to compute Simpson's Approx- imation using n = 100 subintervals. (b) The value of the integral to 10 decimal places is 1.2112096245. Use this value to estimate the error actual - estimate in each of the five approximations