triplequad
Integration of a function dependent on three variables.
q=triplequad(func, x0, x1, y0, y1)
(q, numeval)=triplequad(func, x0, x1, y0, y1,z0,z1, tol)
Inputs
func The function to be integrated.
x0 The lower limit of integration along the x -axis.
x1 The upper limit of integration along the x -axis.
y0 The lower limit of integration along the y -axis.
y1 The upper limit of integration along the y -axis.
z0 The lower limit of integration along the z -axis.
z1 The upper limit of integration along the z -axis.
tol The required accuracy of the solution.
Outputs
q The estimated value of the integral.
numeval The number of function evaluations required to compute the integral.


Description
The integral is computed for the region defined by x0 <= xlim <= x1 , y0 <= ylim <= y1 , and z0 <= zlim <= z1 . To compute integrals in domains which are not cuboids, the parameters y0 , y1 can be defined as functions of xlim , and z0, z1 may be defined as functions of xlim and ylim .
Example
>>// Volume of a sphere
>>triplequad(@(x,y,z)1,-1,1,
>                    @(x)-sqrt(abs(1-x^2)),
>                    @(x)sqrt(abs(1-x^2)), 
>                    @(x,y)-sqrt(abs(1-x^2-y^2)),
>                    @(x,y)sqrt(abs(1-x^2-y^2)))
    4.1888