I've done all bar four questions for an assignment, which I'm stuck on; if anyone could help me or point me in the right direction then I'll be in your debt.

Question 42

(a) Explain why the Simpsonís rule is more accurate than the trapezoidal rule.

I = [Sigma range zero to two] (1.395)sin((pi x^2)/2) dx

Obtain approximate values for the following integral by using:

(b) Simpsonís rule using 8 equal intervals

(c) the 8 point Gauss method

(d) the Romberg method based on Simpsonís rule with 4 and 8 intervals

Alpha = [ 0.101229 0.222381 0.313707 0.362684
0.362684 0.313707 0.222381 0.101229]

x = [-0.960290 -0.796666 -0.525532 -0.183435
0.183435 0.525532 0.796666 0.960290]