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.