# pyramid_integrals

pyramid_integrals, an Octave code which returns the exact value of the integral of any monomial x^i y^j z^k over the interior of the unit pyramid in 3D.

The unit pyramid has a square base of area 4, and a height of 1. Specifically, the integration region is:

```        - ( 1 - Z ) <= X <= 1 - Z
- ( 1 - Z ) <= Y <= 1 - Z
0 <= Z <= 1.
```
The volume of the unit pyramid is 4/3.

### Languages:

pyramid_integrals is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

### Related Data and Programs:

ball_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3d.

circle_integrals, an Octave code which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2d.

cube_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3d.

disk01_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2d.

hexagon_integrals, an Octave code which returns the exact value of the integral of a monomial over the interior of a hexagon in 2d.

hyperball_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit hyperball in m dimensions.

hypercube_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit hypercube in m dimensions.

hypersphere_integrals, an Octave code which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in m dimensions.

line_integrals, an Octave code which returns the exact value of the integral of any monomial over the unit line segment in 1d.

polygon_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of a polygon in 2d.

simplex_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit simplex in m dimensions.

### Source Code:

Last revised on 02 November 2022.