# HYPERCUBE_INTEGRALS Integrals Over the Interior of the Unit Hypercube in M Dimensions

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

The interior of the unit hypercube in M dimensions is defined by

```        0 <= X(1:M) <= 1.
```

The integrands are all of the form

```        F(X) = product ( 1 <= I <= M ) X(I)^E(I)
```
where the exponents are nonnegative integers.

### Languages:

HYPERCUBE_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++ library which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.

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

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

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

HYPERCUBE_GRID, a C++ library which computes a grid of points over the interior of a hypercube in M dimensions.

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

HYPERCUBE_MONTE_CARLO, a C++ library which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit hypercube in M dimensions.

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

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

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

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

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

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

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

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

### List of Routines:

• HYPERCUBE01_MONOMIAL_INTEGRAL: integral inside unit hypercube, M dimensions.
• HYPERCUBE01_SAMPLE samples interior of the unit hypercube in M dimensions.
• HYPERCUBE01_VOLUME: volume of the unit hypercube in M dimensions.
• I4VEC_UNIFORM_AB returns a scaled pseudorandom I4VEC.
• MONOMIAL_VALUE evaluates a monomial.
• R8MAT_UNIFORM_01 fills an R8MAT with unit pseudorandom numbers.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.

Last revised on 19 January 2014.