# hypercube_integrals

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.

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.

### Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

### Languages:

hypercube_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.

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

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 31 October 2022.