circle_integrals, a MATLAB code which returns the exact value of the integral of any monomial along the circumference of the unit circle in 2D.
The circumference of the unit circle in 2D is defined by
x^2 + y^2 = 1
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.
circle_integrals is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
circle_monte_carlo, a MATLAB code which uses the monte carlo method to estimate the integral of a function over the circumference of the unit circle in 2d.
circle_rule, a MATLAB code which computes quadrature rules for the unit circle in 2d, that is, the circumference of the circle of radius 1 and center (0,0).
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.