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 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.
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.
ball_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3d.
circle_integrals, an Octave code which returns the exact value of the integral of any monomial over the surface of the unit circle in 2d.
cube_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3d.
disk_integrals, an Octave 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, an Octave 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, an Octave code which returns the exact value of the integral of a monomial over the interior of a hexagon in 2d.
hyperball_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit hyperball in m dimensions.
hypercube_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit hypercube in m dimensions.
hypersphere_integrals, an Octave code which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in m dimensions.
line_integrals, an Octave code which returns the exact value of the integral of any monomial over the length of the unit line in 1d.
polygon_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of a polygon in 2d.
pyramid_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3d.
simplex_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit simplex in m dimensions.
sphere_integrals, an Octave code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3d.
square_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit square in 2d.
tetrahedron_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.
triangle_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2d.
wedge_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3d.