USE PYTHON to solve this. 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 Approximation 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. USING PYTHON

5. Simpson's Method is another approximation to the integral which uses parabolas instead of lines to approximate f(x): [ f(x) dx = *(f(x0) +2f (11) + 4f(x2) + 2f (x3) + 4f(x4) + ... + 4f (2n-2) + 2f (2n-1) + f(xn)) (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. 5. Simpson's Method is another approximation to the integral which uses parabolas instead of lines to approximate f(x): [ f(x) dx = *(f(x0) +2f (11) + 4f(x2) + 2f (x3) + 4f(x4) + ... + 4f (2n-2) + 2f (2n-1) + f(xn)) (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