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 Simpson’s 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) Simpson’s rule using 8 equal intervals

(c) the 8 point Gauss method

(d) the Romberg method based on Simpson’s 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]