matlab integral3 Vectorized input

In MATLAB, you can use the `integral3` function to compute the triple integral of a function over a 3D region. To handle vectorized input, you can use the `arrayfun` function to apply the `integral3` function to each element of the input arrays.

Here's an example code snippet:

% Define the function to integrate
f = @(x, y, z) x.^2 + y.^2 + z.^2;

% Define the limits of integration
x_min = 0;
x_max = 1;
y_min = 0;
y_max = 1;
z_min = 0;
z_max = 1;

% Create the arrays for the triple integral inputs
x = linspace(x_min, x_max, 100);
y = linspace(y_min, y_max, 100);
z = linspace(z_min, z_max, 100);
[X, Y, Z] = meshgrid(x, y, z);

% Compute the triple integral using arrayfun
dx = x(2) - x(1);
dy = y(2) - y(1);
dz = z(2) - z(1);
integral = dx * dy * dz * sum(arrayfun(@(x, y, z) integral3(f, x_min, x_max, y_min, y_max, z_min, z_max), X, Y, Z));

This code computes the triple integral of the function `f(x, y, z) = x^2 + y^2 + z^2` over the unit cube in three dimensions, using the trapezoidal rule for numerical integration with 100 points along each axis. The input to the function `f` is vectorized using element-wise operations, and the integral is computed by applying the `integral3` function to each element of the input arrays using `arrayfun`. The integral is then computed by summing the results and scaling by the element size.