The problem reads "I must calculate via a quadrature rule of the form that is exact for polynomials with degree lesser or equal to 3."
Attempt: Not much. I don't understand why use the "f(x)" in the expression. Does this mean that f(x) is a polynomial of degree lesser or equal to 1?
The expression must be exact for polynomials up to degree 3. It's equivalent to say it must be exact for , , and . This makes , , and .
Evaluating the expression, I get the following system of equations:
If I understood well, I must solve for , , and ?
The system is not even linear... Hmm. I probably went wrong somewhere. I would appreciate a tip on this one, thanks in advance.