Integrals Along the Length of the Unit Line in 1D

**LINE_INTEGRALS**
is a Python 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 Python library which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.

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

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

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

HYPERBALL_INTEGRALS, a Python 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 Python 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 Python library which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in M dimensions.

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

LINE_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate the integral of a function over the length of the unit line segment in 1D;

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

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

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

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

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

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

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

- i4_uniform_ab.py, returns a scaled uniform I4 between A and B.
- line01_length.py length of the unit line in 1D.
- line01_monomial_integral.py monomial integral over the unit line in 1D.
- line01_sample.py samples the unit line in 1D.
- monomial_value_1d.py evaluates a monomial in 1D.
- r8vec_print.py, prints an R8VEC.
- r8vec_uniform_01.py returns a unit pseudorandom R8VEC.
- r8vec_uniform_ab.py, returns a scaled pseudorandom R8VEC.
- timestamp.py prints the current YMDHMS date as a time stamp.

- line_integrals_test.py, calls all the tests.
- line_integrals_test.sh, runs all the tests.
- line_integrals_test_output.txt, the output file.

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