**line_integrals**,
a C++ code which
returns the exact value of the integral of any monomial
along the length of the unit monomial in 1D.

The length of the unit line in 1D is defined by

0 <= x <= 1

The integrands are all of the form

f(x) = x^ewhere the exponent is a nonnegative integer.

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

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

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_INTEGRALS, a C++ code which returns the exact value of the integral of any monomial 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_FEKETE_RULE, a C++ code which approximates the location of Fekete points in an interval [A,B]. A family of sets of Fekete points, indexed by size N, represents an excellent choice for defining a polynomial interpolant.

LINE_FELIPPA_RULE, a C++ code which returns the points and weights of a Felippa quadrature rule over the interior of a line segment in 1D.

LINE_GRID, a C++ code which computes a grid of points over the interior of a line segment in 1D.

LINE_MONTE_CARLO, a C++ code which uses the Monte Carlo method to estimate the integral of a function over the length of the unit line in 1D.

LINE_NCC_RULE, a C++ code which computes a Newton Cotes Closed (NCC) quadrature rule for the line, that is, for an interval of the form [A,B], using equally spaced points which include the endpoints.

LINE_NCO_RULE, a C++ code which computes a Newton Cotes Open (NCO) quadrature rule, using equally spaced points, over the interior of a line segment 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.

- line_integrals.cpp, the source code.
- line_integrals.sh, compiles the source code.
- line_integrals.hpp, the include file.