6. For each function below, write a program to do Simpson's rule using the sequence of mesh sizes h=(b-a), (b-a), (b-a),..., 2048 (b-a), where b-a is the length of the given interval. Verify that the expected rate of decrease of the error is observed. Comment on any anomolies that are observed. (d) f(x)=√1-2, 1-1, 1], I(f) =π/2; (e) f(x) = e sin(42), [0, ], (f) = (1-e) = 0.2251261368. 7. For each integral Problem 6. how small does h have to ha Algorithm 5.1 Simpson's Rule input a, b, n external f simp f(a) + f (b) h (b a)/n - sum4 0.0 for i-1 to n-1 by 2 do xa+i⭑h sum4 sum4 + f(x) endfor sum2 0.0 for i-2 to n-2 by 2 do xa+i+h sum2 sum2 + f(x) endfor simp (h/3.0)*(simp+4*sum4 +2*sum2) end code I