**annulus_integrals**,
a Python 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^e2where 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 computer code and data files described and made available on this web page are distributed under the MIT license

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

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

ball_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3d.

circle_integrals, a Python code which returns the exact value of the integral of any monomial over the surface of the unit circle in 2d.

cube_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3d.

disk_integrals, a Python code which returns the exact value of the integral of a monomial over the interior of a disk of radius R centered at the origin.

disk01_integrals, a Python code which returns the exact value of the integral of a monomial over the interior of a unit disk centered at the origin in 2d.

hexagon_integrals, a Python code which returns the exact value of the integral of a monomial over the interior of a hexagon in 2d.

hyperball_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit hyperball in m dimensions.

hypercube_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit hypercube in m dimensions.

hypersphere_integrals, a Python code which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in m dimensions.

line_integrals, a Python code which returns the exact value of the integral of any monomial over the length of the unit line in 1d.

polygon_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of a polygon in 2d.

pyramid_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3d.

simplex_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit simplex in m dimensions.

sphere_integrals, a Python code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3d.

square_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit square in 2d.

tetrahedron_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.

triangle_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of an arbitrary triangle in 2d.

triangle01_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.

wedge_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3d.

- annulus_integrals.py, the source code.
- annulus_integrals.sh, runs all the tests.
- annulus_integrals.txt, the output file.