# Documentation

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Numerically evaluate triple integral

`triplequad` will be removed in a future release. Use `integral3` instead.

## Syntax

```q = triplequad(fun,xmin,xmax,ymin,ymax,zmin,zmax) q = triplequad(fun,xmin,xmax,ymin,ymax,zmin,zmax,tol) q = triplequad(fun,xmin,xmax,ymin,ymax,zmin,zmax,tol,method) ```

## Description

`q = 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 first input, `fun`, is a function handle. `fun(x,y,z)` must accept a vector `x` and scalars `y` and `z`, and return a vector of values of the integrand.

Parameterizing Functions explains how to provide additional parameters to the function `fun`, if necessary.

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

`q = 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`.

## Examples

Pass function handle `@integrnd` to `triplequad`:P

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

where the file `integrnd.m` is

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

Pass anonymous function handle `F` to `triplequad`:

```F = @(x,y,z)y*sin(x)+z*cos(x); Q = triplequad(F,0,pi,0,1,-1,1);```

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`.