MATHEMATICS LAB
Numerical Integration
Approximate a definite integral and see how numerical methods estimate its value and reduce the error.
Result
Numerical approximation
Step size h
Estimated reference value
Difference from reference
Alternative-grid check
Diagnostic comparison, not an error bound. Different sampling grids may yield substantially different estimates.
| Subintervals | Method | Approximation | Difference from selected grid |
|---|
Geometric representation
The orange curve represents f(x). The blue regions show the selected method’s geometric approximation; for Simpson’s rules, these are interpolating polynomials, not the original curve.
Step-by-step calculation
Sample table
Displayed values are rounded for readability; calculations use the numerical engine’s full precision.
| i | xᵢ | f(xᵢ) | Weight | Weight × f(xᵢ) | Cumulative sum |
|---|
Method comparison
| Method | Approximation | Difference from reference |
|---|
Convergence as n increases
The plot compares differences from a numerical reference; it does not establish convergence.