3. There is a method for estimating a definite integral similar to Simpson's rule which we will call Paul's Peculiar Rule. It requires that we divide the interval into a number of subintervals divisible by four. Then, n//4-1 So f(x) dx = 25 (- f(a) f(b) + 16 [ f(+ak+1) -12 [ f(Tax+2) + 16 [ f(Tak+3) 2 [ f(Tak)) n//4-1 ke=0 n//4-1 n//4-1 k=0 k=0 k=1 (a) Write a short python program called PPR(a,b,n,f,F) which estimates S f (2)dt according to Paul's Peculiar Rule using n subintervals. Warning: Watch out for the very last sum. It starts at k=1 while all the others start at k=0. (b) For the integral: dr make a table comparing the errors of estimating this integral with the Trapezoid Rule, Simpson's Rule, and Paul's Peculiar Rule for n = 12, 120, 1200 subintervals. (C) What is the order of the error for Paul's Peculiar Rule? How do you know