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<html>
<head>
<title>
LINE_INTEGRALS - Integrals Along the Length of the Unit Line in 1D
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
LINE_INTEGRALS <br> Integrals Along the Length of the Unit Line in 1D
</h1>
<hr>
<p>
<b>LINE_INTEGRALS</b>
is a MATLAB library which
returns the exact value of the integral of any monomial
along the length of the unit monomial in 1D.
</p>
<p>
The length of the unit line in 1D is defined by
<pre>
0 <= x <= 1
</pre>
</p>
<p>
The integrands are all of the form
<pre>
f(x) = x^e
</pre>
where the exponent is a nonnegative integer.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>LINE_INTEGRALS</b> is available in
<a href = "../../c_src/line_integrals/line_integrals.html">a C version</a> and
<a href = "../../cpp_src/line_integrals/line_integrals.html">a C++ version</a> and
<a href = "../../f77_src/line_integrals/line_integrals.html">a FORTRAN77 version</a> and
<a href = "../../f_src/line_integrals/line_integrals.html">a FORTRAN90 version</a> and
<a href = "../../m_src/line_integrals/line_integrals.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/ball_integrals/ball_integrals.html">
BALL_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the interior of the unit ball in 3D.
</p>
<p>
<a href = "../../m_src/circle_integrals/circle_integrals.html">
CIRCLE_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the circumference of the unit circle in 2D.
</p>
<p>
<a href = "../../m_src/cube_integrals/cube_integrals.html">
CUBE_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the interior of the unit cube in 3D.
</p>
<p>
<a href = "../../m_src/disk_integrals/disk_integrals.html">
DISK_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the interior of the unit disk in 2D.
</p>
<p>
<a href = "../../m_src/hyperball_integrals/hyperball_integrals.html">
HYPERBALL_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the interior of the unit hyperball in M dimensions.
</p>
<p>
<a href = "../../m_src/hypercube_integrals/hypercube_integrals.html">
HYPERCUBE_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the interior of the unit hypercube in M dimensions.
</p>
<p>
<a href = "../../m_src/hypersphere_integrals/hypersphere_integrals.html">
HYPERSPHERE_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the surface of the unit hypersphere in M dimensions.
</p>
<p>
<a href = "../../m_src/line_fekete_rule/line_fekete_rule.html">
LINE_FEKETE_RULE</a>,
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.
</p>
<p>
<a href = "../../m_src/line_felippa_rule/line_felippa_rule.html">
LINE_FELIPPA_RULE</a>,
a MATLAB library which
returns the points and weights of a Felippa quadrature rule
over the interior of a line segment in 1D.
</p>
<p>
<a href = "../../m_src/line_grid/line_grid.html">
LINE_GRID</a>,
a MATLAB library which
computes a grid of points
over the interior of a line segment in 1D.
</p>
<p>
<a href = "../../m_src/line_monte_carlo/line_monte_carlo.html">
LINE_MONTE_CARLO</a>,
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.
</p>
<p>
<a href = "../../m_src/line_ncc_rule/line_ncc_rule.html">
LINE_NCC_RULE</a>,
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.
</p>
<p>
<a href = "../../m_src/line_nco_rule/line_nco_rule.html">
LINE_NCO_RULE</a>,
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.
</p>
<p>
<a href = "../../m_src/polygon_integrals/polygon_integrals.html">
POLYGON_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the interior of a polygon in 2D.
</p>
<p>
<a href = "../../m_src/pyramid_integrals/pyramid_integrals.html">
PYRAMID_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the interior of the unit pyramid in 3D.
</p>
<p>
<a href = "../../m_src/simplex_integrals/simplex_integrals.html">
SIMPLEX_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the interior of the unit simplex in M dimensions.
</p>
<p>
<a href = "../../m_src/sphere_integrals/sphere_integrals.html">
SPHERE_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the surface of the unit sphere in 3D.
</p>
<p>
<a href = "../../m_src/square_integrals/square_integrals.html">
SQUARE_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the interior of the unit square in 2D.
</p>
<p>
<a href = "../../m_src/tetrahedron_integrals/tetrahedron_integrals.html">
TETRAHEDRON_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the interior of the unit tetrahedron in 3D.
</p>
<p>
<a href = "../../m_src/triangle_integrals/triangle_integrals.html">
TRIANGLE_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the interior of the unit triangle in 2D.
</p>
<p>
<a href = "../../m_src/wedge_integrals/wedge_integrals.html">
WEDGE_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the interior of the unit wedge in 3D.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "line01_length.m">line01_length.m</a>
length of the unit line in 1D.
</li>
<li>
<a href = "line01_monomial_integral.m">line01_monomial_integral.m</a>
monomial integral over the unit line in 1D.
</li>
<li>
<a href = "line01_sample.m">line01_sample.m</a>
samples the unit line in 1D.
</li>
<li>
<a href = "monomial_value_1d.m">monomial_value_1d.m</a>
evaluates a monomial in 1D.
</li>
<li>
<a href = "r8vec_uniform_01.m">r8vec_uniform_01.m</a>
returns a unit pseudorandom R8VEC.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>
prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "line_integrals_test.m">line_integrals_test.m</a>,
a sample calling program.
</li>
<li>
<a href = "line_integrals_test01.m">line_integrals_test01.m</a>,
estimates several integrals using the Monte Carlo method.
</li>
<li>
<a href = "line_integrals_test_output.txt">line_integrals_test_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 17 January 2014.
</i>
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