MATLAB Function Reference |
Numerically evaluate double integral
Syntax
q = dblquad(fun,xmin,xmax,ymin,ymax) q = dblquad(fun,xmin,xmax,ymin,ymax,tol) q = dblquad(fun,xmin,xmax,ymin,ymax,tol,method)
Description
q = dblquad(fun,xmin,xmax,ymin,ymax)
calls the quad
function to evaluate the double integral fun(x,y)
over the rectangle xmin <= x <= xmax
, ymin <= y <= ymax
. fun
is a function handle. See Function Handles in the MATLAB Programming documentation for more information. fun(x,y)
must accept a vector x
and a scalar y
and return a vector of values of the integrand.
Parameterizing Functions Called by Function Functions, in the MATLAB mathematics documentation, explains how to provide additional parameters to the function fun
, if necessary.
q = dblquad(fun,xmin,xmax,ymin,ymax,tol)
uses a tolerance tol
instead of the default, which is 1.0e-6
.
q = dblquad(fun,xmin,xmax,ymin,ymax,tol,method)
uses the quadrature function specified as method
, instead of the default quad
. Valid values for method
are @quadl
or the function handle of a user-defined quadrature method that has the same calling sequence as quad
and quadl
.
Example
Pass M-file function handle @integrnd
to dblquad
:
where the M-file integrnd.m
is
Pass anonymous function handle F
to dblquad
:
The integrnd
function integrates y*sin(x)+x*cos(y)
over the square pi <= x <= 2*pi
, 0 <= y <= pi
. Note that the integrand can be evaluated with a vector x
and a scalar y
.
Nonsquare regions can be handled by setting the integrand to zero outside of the region. For example, the volume of a hemisphere is
See Also
quad
, quadl
, triplequad
, function_handle
(@
), anonymous functions
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