I was just wondering if I could have some assistance in regards to the Trapezoidal Rule and Simpson's Rule.
I have a question where it asks to generalize the Trapezoidal Rule to the case of Simpson's Rule - which the aim is to compute further approximations without having to recalculate any f's. Apparently we have to start with Richardson extrapolation to show how it can be derived.
Trapezoidal Rule: I[2n] (a,b)=1/2 I[n] (a,b)+(b-a)/2N f(x[2j+1])
Many thanks, !