SEMICIRCLE_INTEGRALS is a Mathematica notebook which evaluates the integral of a function f(x,y) over the interior of the unit semicircle -1 <= x <= +1, 0 <= y <= sqrt ( 1-x^2).
In particular, the notebook contains results from integrating the "interesting" monomials up to degree 6. (The non-interesting ones, which have x to an odd power, integrate to zero over this region.)
The motivation for this computation was the need to check the monomial exactness of quadrature rules designed for a circular sector.
Similar calculations of monomial integrals for the circle and the quadrant are included.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
QUADRULE is a MATHEMATICA library which contains some scripts used to evaluate quadrature rules needed for the C, C++, FORTRAN90 and MATLAB QUADRULE libraries.
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