# cube_integrals

cube_integrals, a C code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.

The interior of the unit cube in 3D is defined by

```        0 <= X <= 1,
0 <= Y <= 1,
0 <= Z <= 1.
```

The integrands are all of the form

```        f(x,y,z) = x^e1 * y^e2 * z^e3.
```
where the exponents are nonnegative integers.

### Languages:

cube_integrals is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

### Related Data and Programs:

BALL_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.

CIRCLE_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2D.

CUBE_ARBQ_RULE, a C code which returns quadrature rules, with exactness up to total degree 15, over the interior of the symmetric cube in 3D, by Hong Xiao and Zydrunas Gimbutas.

CUBE_EXACTNESS, a C code which investigates the polynomial exactness of quadrature rules over the interior of a cube in 3D.

CUBE_FELIPPA_RULE, a C code which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.

CUBE_GRID, a C code which computes a grid of points over the interior of a cube in 3D.

CUBE_MONTE_CARLO, a C code which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit cube in 3D.

DISK01_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2D.

HYPERBALL_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit hyperball in M dimensions.

HYPERCUBE_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit hypercube in M dimensions.

HYPERSPHERE_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in M dimensions.

LINE_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the length of the unit line in 1D.

POLYGON_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.

PYRAMID_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.

SIMPLEX_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit simplex in M dimensions.

SPHERE_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3D.

SQUARE_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit square in 2D.

TETRAHEDRON_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.

TRIANGLE_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.

WEDGE_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.

### Source Code:

Last revised on 16 June 2019.