**line_integrals**,
an Octave 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
an Octave version and
a Python version.

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.

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.

line_fekete_rule, an Octave 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, an Octave code which returns the points and weights of a felippa quadrature rule over the interior of a line segment in 1d.

line_grid, an Octave code which computes a grid of points over the interior of a line segment 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.

- line01_length.m length of the unit line in 1D.
- line01_monomial_integral.m monomial integral over the unit line in 1D.
- line01_sample.m samples the unit line in 1D.
- monomial_value_1d.m evaluates a monomial in 1D.