Numerical Integration: Understanding Error, Big Oh and Taylor Expansion

[Feldoh]

We've covering numerical integration in one of my classes this semester, however I'm sort of at a loss as to how to deal with error in when using a taylor expansion for numerical integration, and also order of method (Big Oh?) and what exactly it means and was wondering if anyone could explain some of this to me or suggest some websites which covers this type of material?

 

[MathematicalPhysicist]

Be more specific, big O means that in a neighbourhood of x->x0 f(x)=O(g(x)) iff there exists M>0 s.t |f(x)/g(x)|<=M.
I forgot what theta means, but searching the web shouldn't be a problem for you is it?