## numerical analysis (romberg/newton cotes)

Consider the following two methods for approximating
I=int(f(x)dx, x=a..b)

(a)use of noncomposite closed Newton-Cotes formulas for n=2,3,4,...
(b)use of Romberg integration;let R[n,n] ; n=1,2,3,4,... denote the "diagonal" entries of the Romberg table

--with regard to convergence of the sequences of computed approximations in (a) and (b) as n->infinity, why is (b) preferable to (a)?

so this is a question from a review pack for an exam and I just don't know. I know that the closed newton cotes has a large degree of accuracy but I am not sure why using Romberg integration is preferable

any help would be awsome... Thanx