| \( N \) | \( I \) | \( \sigma_N \) |
| 10 | 3.10263E+00 | 3.98802E-01 |
| 100 | 3.02933E+00 | 4.04822E-01 |
| 1000 | 3.13395E+00 | 4.22881E-01 |
| 10000 | 3.14195E+00 | 4.11195E-01 |
| 100000 | 3.14003E+00 | 4.14114E-01 |
| 1000000 | 3.14213E+00 | 4.13838E-01 |
| 10000000 | 3.14177E+00 | 4.13523E-01 |
| \( 10^{9} \) | 3.14162E+00 | 4.13581E-01 |
We note that as \( N \) increases, the integral itself never reaches more than an agreement to the fourth or fifth digit. The variance also oscillates around its exact value \( 4.13581E-01 \).