# LINE_INTEGRALS 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^e
```
where the exponent is a nonnegative integer.

### Languages:

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.

### Related Data and Programs:

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.

### Examples and Tests:

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

Last revised on 22 June 2015.