The sphere in 1 dimension is just the line segment that runs from -1 to 1. It`s volume (1-dimensional integral) is just 2. In this case, the Monte-Carlo method will be exact (even with ONE point!) because in this case, the unit sphere is exactly the same as the ''box`` with side 2. Here is the uninteresting output from my program:
--------------------------------------------- VALUES AVERAGED OVER ALL PROCESSORS: volume of 1 sphere is 2.0000000000000000e+00 st. dev. is 0.0000000000000000e+00 total number of points: 4000 ---------------------------------------------