q = integral2(fun, xmin, xmax, ymin, ymax)
q = integral2(fun, xmin, xmax, ymin, ymax, name, value)
| Parameter | Description |
|---|---|
| fun | Integrand: function handle of two variables. |
| xmin, xmax | Limits of integration in x: real or infinite scalars. |
| ymin, ymax | Limits of integration in y: real scalars or function handles of x. |
| name, value | One or more name/value pairs: 'RelativeTolerance', 'AbsoluteTolerance', 'Vectorized', 'Waypoints'. |
| Parameter | Description |
|---|---|
| q | Value of the double integral. |
q = integral2(fun, xmin, xmax, ymin, ymax) numerically integrates the function fun(x, y) over the region xmin <= x <= xmax and ymin(x) <= y <= ymax(x).
The y limits ymin and ymax may be scalars, or function handles of x to describe a non-rectangular region.
The integration is performed with nested adaptive Gauss-Kronrod quadrature. The name/value pairs RelativeTolerance (default 1e-6) and AbsoluteTolerance (default 1e-10) control the accuracy; the former names RelTol and AbsTol are still accepted.
By default (Vectorized set to true) fun must accept arrays and operate element-wise. Set Vectorized to false when fun accepts only scalar arguments: it is then evaluated point by point, which is slower.
Waypoints specifies points of interest of the integration region, such as local extrema or discontinuities, that the integrator uses in its initial mesh: a two-column array [x y] of points, or a cell array {x y} of grid vectors. The x interval is split at the x values of the waypoints, and each y interval at their y values. Waypoints must be real and finite. Do not use waypoints to specify singularities; split the region instead.
q = integral2(@(x, y) x .* y, 0, 1, 0, 1)q = integral2(@(x, y) x .* y, 0, 1, 0, @(x) x)fun = @(x, y) log(x^2 + y^2);
q = integral2(fun, 0, 2, 0, 2, 'Vectorized', false)fun = @(x, y) abs(x - 0.3) .* abs(y - 0.6);
q = integral2(fun, 0, 1, 0, 1, 'Waypoints', [0.3, 0.6])| Version | Description |
|---|---|
| 2.0.0 | initial version |
| 2.0.0 | 'Vectorized' option added: integrate functions written for scalar inputs. |
| 2.0.0 | 'AbsoluteTolerance' and 'RelativeTolerance' names added ('AbsTol' and 'RelTol' still accepted). |
| 2.0.0 | 'Waypoints' option added: points of interest in the integration region. |