# line_integrals

line_integrals, a MATLAB 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^e
```
where the exponent is a nonnegative integer.

### Languages:

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

### Related Data and Programs:

ball_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3d.

circle_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2d.

cube_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3d.

disk01_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2d.

hexagon_integrals, a MATLAB code which returns the exact value of the integral of a monomial over the interior of a hexagon in 2d.

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

line_grid, a MATLAB code which computes a grid of points over the interior of a line segment in 1d.

line_monte_carlo, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB code which returns the exact value of the integral of any monomial over the interior of a polygon in 2d.

pyramid_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3d.

simplex_integrals, a MATLAB 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 MATLAB code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3d.

square_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit square in 2d.

tetrahedron_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.

triangle_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2d.

wedge_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3d.

### Source Code:

Last revised on 15 February 2019.