disk01_integrals

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.

The interior of the unit disk in 2D is defined by

        x^2 + y^2 <= 1

The integrands are all of the form

        f(x,y) = x^e1 * y^e2

where the exponents are nonnegative integers. If any exponent is an odd integer, the integral will be zero. Thus, the "interesting" results occur when all exponents are even.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

disk01_integrals is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

disk01_monte_carlo, a MATLAB code which uses the monte carlo method to estimate the integral of a function over the interior of the unit disk in 2d.

disk01_rule, a MATLAB code which computes quadrature rules for the unit disk in 2d.

matlab_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the surface or interior of some geometric object, including a line, quadrilateral, box, circle, disk, sphere, ball and others.

Reference:

Gerald Folland,
How to Integrate a Polynomial Over a Sphere,
American Mathematical Monthly,
Volume 108, Number 5, May 2001, pages 446-448.

Source Code:

disk01_area.m, returns the area of the unit disk.
disk01_monomial_integral.m, returns the exact integral of a monomial over the unit disk
disk01_sample.m, returns uniform sample points from the unit disk.
monomial_value.m, evaluates a monomial function.

Last revised on 07 January 2019.