The suffix cr stands for the brute force approach while is stands for the use of importance sampling. All calculations use ran0 as function to generate the uniform distribution.
| N | I_{cr} | \sigma_{cr} | I_{is} | \sigma_{is} |
| 10000 | 3.13395E+00 | 4.22881E-01 | 3.14163E+00 | 6.49921E-03 |
| 100000 | 3.14195E+00 | 4.11195E-01 | 3.14163E+00 | 6.36837E-03 |
| 1000000 | 3.14003E+00 | 4.14114E-01 | 3.14128E+00 | 6.39217E-03 |
| 10000000 | 3.14213E+00 | 4.13838E-01 | 3.14160E+00 | 6.40784E-03 |
However, it is unfair to study one-dimensional integrals with MC methods!