I was hoping someone could help me or direct me to some reference for exploring the relationship between Midpoint and Simpson's approximations and accuracy of methods: En = Cn^p.
For example, I have calculated 3 approximations with decreasing n using each strategy.
I = integral( f(x) dx) from 0 to 1
Mn is a midpoint approximation
En = | I - Mn |
Then using the relationship En = Cn^p I am to determine the value of the constants C and p.
I can't figure this out and I've been trying and searching for similar examples for hours.
Thanks.