Simpson's rule, 8 point Gauss method and Romberg method
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.
(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]