perform gaussian quadrature in matlab

In order to perform Gaussian quadrature in MATLAB, you can use the gaussquad function which can be found in the Symbolic Math Toolbox. This function computes the quadrature weights and quadrature points for you.

Here's an example code snippet that demonstrates how to use gaussquad to approximate the definite integral of a given function:

main.m
% Define the function to integrate
f = @(x) exp(-x.^2);

% Define the interval of integration
a = 0;
b = 1;

% Choose the number of quadrature points to use
n = 5;

% Compute the quadrature weights and points using gaussquad
[pts, wts] = gaussquad(n, 'leg');

% Evaluate the function at the quadrature points
fx = f((b-a)/2 .* pts + (a+b)/2);

% Compute the approximate integral
approx_int = (b-a)/2 .* dot(wts, fx)
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In this example, we define the function f(x) = exp(-x^2), the interval of integration [0,1], and specify that we want to use 5 quadrature points (which corresponds to a degree-4 Gaussian quadrature rule). The gaussquad function is used to compute the quadrature weights wts and quadrature points pts using the Legendre polynomial family. We then evaluate the function at the quadrature points and use the dot product to compute the approximate integral. Note that we need to scale the quadrature points and weights by (b-a)/2 because Gaussian quadrature is defined on the interval [-1,1].