The Gauss Legendre quadrature method...
Legendre-Gauss Quadrature -- from Wolfram MathWorld
... compute a definite integral as...
(1)
... and the result is exact if f(x) is a polynomial of degree . For n=2 and ...
Kind regards
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.
The Gauss Legendre quadrature method...
Legendre-Gauss Quadrature -- from Wolfram MathWorld
... compute a definite integral as...
(1)
... and the result is exact if f(x) is a polynomial of degree . For n=2 and ...
Kind regards
Thanks chisigma, I appreciate your help. I looked into mathworld but didn't understand how you found that the formula is exact for a polynomial of degree lesser or equal than 2n-1. Nor do I know how you found out x_i and a_i.
I've searched into wikipedia about Gaussian quadrature and they indeed find the same values. It seems I must dig into Legrendre's polynomials in order to understand what's going on.
Also, I don't know what's wrong with my method. Could you tell me what did I do wrong?!