Editing Gaussian quadrature (section)

== Change of interval ==
An integral over {{math|[''a'', ''b'']}} must be changed into an integral over {{math|[−1, 1]}} before applying the Gaussian quadrature rule. This change of interval can be done in the following way:
<math display="block">\int_a^b f(x)\,dx = \int_{ -1}^1 f\left(\frac{b-a}{2}\xi + \frac{a+b}{2}\right)\,\frac{dx}{d\xi}d\xi</math>

with <math>\frac{dx}{d\xi} = \frac{b-a}{2}</math>

Applying the <math>n</math> point Gaussian quadrature <math>(\xi, w)</math> rule then results in the following approximation:
<math display="block">\int_a^b f(x)\,dx \approx \frac{b-a}{2} \sum_{i=1}^n w_i f\left(\frac{b-a}{2}\xi_i + \frac{a+b}{2}\right).</math>