In this exercise Romberg rules are derived. Assume that I(n) is an integration rule that uses n subintervals and h is the corresponding width of each subinterval. (a) It is known that the error term for the composite Simpson’s rule involves even powers of h. In particular, b a f(x)dx = IS(n) + αh4 + βh6 + γh8 + · · · . Show that the integration rule IR = 1 15 [16IS(2n) − IS(n)] has an error that is O(h6).