annulus_integrals

annulus_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of an annulus centered at the origin.

The interior of the disk is defined by

        r1^2 <= x^2 + y^2 <= r2^2

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:

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

Related Data and Programs:

annulus_integrals_test

annulus_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate the integral of a function over the interior of an annulus centered at the origin.

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.

Source Code:

annulus_area.m, returns the area of an annulus centered at the origin.
annulus_monomial_integral.m, returns the exact integral of a monomial over an annulus centered at the origin.
annulus_sample.m, returns uniform sample points from an annulus centered at the origin.
monomial_value.m, evaluates a monomial function.

Last revised on 04 November 2022.