Demonstration of Gaussian Quadrature
The second table however shows that for smaller integration intervals, both the trapezoidal rule
and Simpson's method compare well with the results obtained with the Gauss-Legendre
approach.
| \( N \) | Trapez | Simpson | Gauss-Legendre |
| 10 | 0.798861 | 0.799231 | 0.799233 |
| 20 | 0.799140 | 0.799233 | 0.799233 |
| 40 | 0.799209 | 0.799233 | 0.799233 |
| 100 | 0.799229 | 0.799233 | 0.799233 |
| 1000 | 0.799233 | 0.799233 | 0.799233 |