p>

    <p>
      A <i>standard Gauss-Legendre quadrature rule</i> is a set of <b>n</b>
      positive weights <b>w</b> and abscissas <b>x</b> so that
      <pre>
        Integral ( -1 &lt;= x &lt;= +1 ) f(x) dx
      </pre>
      may be approximated by
      <pre>
        Sum ( 1 &lt;= I &lt;= N ) w(i) * f(x(i))
      </pre>
    </p>

    <p>
      For a standard Gauss-Legendre rule, polynomial exactness is defined in terms of
      the function <b>f(x)</b>.  That is, we say the rule is exact for polynomia