`integral3`

Numerical triple integral over a box or a region with variable limits.

Category: Mathematics > Numerical Integration and Differential Equations

Syntax

q = integral3(fun, xmin, xmax, ymin, ymax, zmin, zmax)

Integrates fun(x, y, z) over a box.

q = integral3(___, Name, Value)

Sets options such as 'AbsTol', 'RelTol' and 'Method'.

Description

The method is the three-dimensional analogue of integral2, based on nested adaptive quadrature. The cost grows quickly with the dimension, so smooth integrands and moderate tolerances are advisable.

Use element-wise operators in the integrand.

Input arguments

fun: Handle w = fun(x, y, z) that accepts arrays of the same size and returns an array of that size.
xmin ... zmax: Scalar limits; the y limits may be handles of x, and the z limits handles of x and y.

Output arguments

q: Approximate value of the integral.

Example

Integral of x + y + z on the unit cube

integral3(@(x, y, z) x + y + z, 0, 1, 0, 1, 0, 1)

Output

ans = 1.5000

integral3