We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now you are asked to implement the Simpson rule, where we approximate the integration of a non-linear...

Extracted text: We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now you are asked to implement the Simpson rule, where we approximate the integration of a non-linear curve using piecewise quadratic functions. Assume f(x) is continuous over [a, b] . Let [a, b] be divided into N subintervals, each of length Ax, with endpoints at P = x0, x1, X2, ..., Xn,..., XN. Each interval is Ax = (b – a)/N. The Simpon numerical integration rule is derived as: N-2 Li f(x)dx = * f(x0) + 4 (2n odd f(xn)) + 2 ( En=2,n even N-1 f(x,) + f(xn)] . Now complete the Python function InterageSimpson(N, a, b) below to implement this Simpson rule using the above equation. The function to be intergrate is f (x) = 2x³ (Already defined, don't change it). In [ ]: # Complete the function given the variables N,a,b and return the value as "TotalArea". # Don't change the predefined content, only fill your code in the region "YOUR CODE" from math import * def InterageSimpson (N, a, b): # n is the total intervals, a and b is the lower and upper bound respectively """Hint: Use loop to add all the values in the above equation and use the if statement to determine whether the value is odd or even" "" def f(x): ## The function f(x)=2*x**3 is defined as below, DON'T CHANGE IT: f=2*x**3 return f value=0 # Initial value TotalArea=0 # TotalArea as the final integral value, the area underneath the curve. dx= (b-a)/N # delta x, the interval length # Complete the function by filling your codes below: # your code here return TotalArea # Make sure in your solution, you use the same name "TotalArea" for the output