MATLAB Function Reference

triplequad

Numerically evaluate triple integral

Syntax

• triplequad(fun,xmin,xmax,ymin,ymax,zmin,zmax)
  triplequad(fun,xmin,xmax,ymin,ymax,zmin,zmax,tol)
  triplequad(fun,xmin,xmax,ymin,ymax,zmin,zmax,tol,method)
  triplequad(fun,xmin,xmax,ymin,ymax,zmin,zmax,tol,method,p1,p2,...)
  

Description

triplequad(fun,xmin,xmax,ymin,ymax,zmin,zmax) evaluates the triple integral fun(x,y,z) over the three dimensional rectangular region xmin <= x <= xmax, ymin <= y <= ymax, zmin <= z <= zmax. The function fun(x,y,z) must accept a vector x and scalars y and z, and return a vector of values of the integrand.

triplequad(fun,xmin,xmax,ymin,ymax,zmin,zmax,tol) uses a tolerance tol instead of the default, which is 1.0e-6.

triplequad(fun,xmin,xmax,ymin,ymax,zmin,zmax,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.

triplequad(fun,xmin,xmax,ymin,ymax,zmin,zmax,tol,method,p1,p2,...) passes the additional parameters p1,p2,... to fun(x,y,p1,p2,...). Use [] as a placeholder if you do not specify tol or method. triplequad(fun,xmin,xmax,ymin,ymax,zmin,zmax,[],[],p1,p2,...) is the same as triplequad(fun,xmin,xmax,ymin,ymax,zmin,zmax,1e-6,@quad,p1,p2,...)

Examples

fun can be an inline object

• Q = triplequad(inline('y*sin(x)+z*cos(x)'),0,pi,0,1,-1,1)
  

or a function handle

• Q = triplequad(@integrnd,0,pi,0,1,-1,1)
  

where integrnd.m is the M-file

• function f = integrnd(x,y,z)
  f = y*sin(x)+z*cos(x);
  

This example integrates y*sin(x)+z*cos(x) over the region 0 <= x <= pi, 0 <= y <= 1, -1 <= z <= 1. Note that the integrand can be evaluated with a vector x and scalars y and z.

See Also

dblquad, inline, quad, quadl, @ (function handle)

trimesh

triplot