Integrals Along the Length of the Unit Line in 1D

**LINE_INTEGRALS**
is a MATLAB library 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 GNU LGPL license.

**LINE_INTEGRALS** is available in
a C version and
a C++ version and
a FORTRAN77 version and
a FORTRAN90 version and
a MATLAB version and
a Python version.

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

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

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

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

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

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

HYPERSPHERE_INTEGRALS, a MATLAB library 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 MATLAB library 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 MATLAB library which returns the points and weights of a Felippa quadrature rule over the interior of a line segment in 1D.

LINE_GRID, a MATLAB library which computes a grid of points over the interior of a line segment in 1D.

LINE_MONTE_CARLO, a MATLAB library 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 MATLAB library 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 MATLAB library 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 MATLAB library which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.

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

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

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

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

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

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

- 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.
- r8vec_uniform_01.m returns a unit pseudorandom R8VEC.
- timestamp.m prints the current YMDHMS date as a time stamp.

- line_integrals_test.m, a sample calling program.
- line_integrals_test01.m, estimates several integrals using the Monte Carlo method.
- line_integrals_test_output.txt, the output file.

You can go up one level to the MATLAB source codes.