Trapezoidal rule: T = (h/2)[f(a)+2Σf(xᵢ)+f(b)] where h=(b−a)/n. Error ≤ (b−a)³/(12n²)·max|f″|. More accurate than left/right Riemann sums. Simpson's rule (using parabolas) is even more accurate: S = (h/3)[f(a)+4f(x₁)+2f(x₂)+...+f(b)].
How to Use
Set up the integral:
- Function: Choose from presets
- Bounds: a and b
- Subdivisions: n trapezoids
Error Analysis
- Error = O(h²) — doubles n, cuts error by 4
- Exact for linear functions
- Simpson: O(h⁴) — much more accurate
Composite Formula
Split [a,b] into n equal parts. Each trapezoid has width h. Interior points are counted twice (shared edges). End points counted once.
Step-by-Step Instructions
- 1Select a function.
- 2Set lower bound a.
- 3Set upper bound b.
- 4Choose number of subdivisions.
- 5Compare with Simpson's rule.