Gaussian quadrature rules attempt to give the most accurate possible formulae by choosing the quadrature points x_{i} and weights w_{i} to give exact results for polynomials of the highest degree possible. For quadrature of a function of one variable, n Gaussian quadrature points will give accurate integrals for all polynomials of degree up to 2n  1.
In one dimension, on the domain (1, 1), some low order polynomials can be integrated as follows:
Number of points  Quadrature weights  Quadrature points 

1  2  0 
2  1, 1  1/√3, 1/√3 
3  5/9, 8/9, 5/9  √(3/5), 0, √(3/5) 
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