Integration

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);