# Gaussian quadrature with change of variables

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Melanie Wroblewski on 29 Nov 2022
I need help writing a matlab function that numerically integrates any continuous function f (x, y) over the parallelogram (1, 1), (3, 2), (4, 4) and (6, 5) using Gaussian quadrature with m × n points. The inputs of your function must be f , m and n.

Andreas Apostolatos on 29 Nov 2022
Hi Melanie,
There are serveral submissions on File Exchange that you can use to compute integrals using the Gauss Quadrature rule. Please check the following post on MATLAB Answers and in particular the comprehensive answer from John D'Errico:
Among other, he also shows comprehensive examples on how this can be done for one-dimensional functions f(x). For two-dimensional functions f(x,y) you simply needed a nested loop. This is also very nicely shown in the following MATLAB Answers post,
I hope this helps.
Kind regards
Andreas

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