. The Gaussian quadrature rule having w ( x ) = 1 for integrals on [−1 , 1] (cf. Table 5.6) is called Gauss–Legendre quadrature because it relies on the Legendre polynomials. The nodes and weights for...

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The Gaussian quadrature rule having
w(x) = 1 for integrals on [−1,
1] (cf. Table 5.6) is called
Gauss–Legendre quadrature
because it relies on the Legendre polynomials. The nodes and weights for the 10-point Gauss–Legendre rule are given.

a.
Plot the weights versus the nodes.

b.
Find the area under the curve
y
=
x2 between −1 and 1. Compare this with the exact answer and comment on the precision of this quadrature technique.