disk_integrals

disk_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of a disk of radius R centered at the origin in 2D.

The interior of the disk is defined by

        x^2 + y^2 <= r^2

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:

disk_integrals is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

disk_integrals_test

disk_monte_carlo, an Octave code which uses the Monte Carlo method to estimate the integral of a function over the interior of a disk of radius R centered at the origin.

octave_integrals, an Octave 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:

disk_area.m, returns the area of a disk of radius R centered at the origin.
disk_monomial_integral.m, returns the exact integral of a monomial over a disk of radius R centered at the origin.
disk_sample.m, returns uniform sample points from disk of radius R centered at the origin.
monomial_value.m, evaluates a monomial function.

Last revised on 04 November 2022.