MATLAB LanguageIntegration

Integral, integral2, integral3

1 dimensional

To integrate a one dimensional function

``````f = @(x) sin(x).^3 + 1;
``````

within the range

``````xmin = 2;
xmax = 8;
``````

one can call the function

``````q = integral(f,xmin,xmax);
``````

it's also possible to set boundarys for relative and absolute errors

``````q = integral(f,xmin,xmax, 'RelTol',10e-6, 'AbsTol',10-4);
``````

2 dimensional

If one wants to integrate a two dimensional function

``````f = @(x,y) sin(x).^y ;
``````

within the range

``````xmin = 2;
xmax = 8;
ymin = 1;
ymax = 4;
``````

one calls the function

``````q = integral2(f,xmin,xmax,ymin,ymax);
``````

Like in the other case it's possible to limit the tolerances

``````q = integral2(f,xmin,xmax,ymin,ymax, 'RelTol',10e-6, 'AbsTol',10-4);
``````

3 dimensional

Integrating a three dimensional function

``````f = @(x,y,z) sin(x).^y - cos(z) ;
``````

within the range

``````xmin = 2;
xmax = 8;
ymin = 1;
ymax = 4;
zmin = 6;
zmax = 13;
``````

is performed by calling

``````q = integral3(f,xmin,xmax,ymin,ymax, zmin, zmax);
``````

Again it's possible to limit the tolerances

``````q = integral3(f,xmin,xmax,ymin,ymax, zmin, zmax, 'RelTol',10e-6, 'AbsTol',10-4);
``````