annulus_integrals, an Octave 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.
The information on this web page is distributed under the MIT license.
annulus_integrals is available in a MATLAB version and an Octave version and a Python version.
annulus_monte_carlo, an Octave code which uses the Monte Carlo method to estimate the integral of a function over the interior of an annulus 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.