disk_integrals, a MATLAB 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^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
disk_integrals is available in a MATLAB version.
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cube_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3d.
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sphere_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3d.
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tetrahedron_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.
triangle_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2d.
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