integration

Numerical Integration

Approximates definite integrals using four different methods.

Methods

1. Rectangle (Underestimate) - uses left endpoints
2. Rectangle (Overestimate) - uses right endpoints
3. Trapezoid Method - averages left and right endpoints
4. Simpson's Method - uses parabolic approximation

Usage

1. Create test.txt with equally spaced data points (y-values):

   x1 y1
   x2 y2
   ...
   

   Default step size: 0.5

2. Compile:

   g++ -o main main.cpp

3. Run and choose method (1-4):

   ./main

Formulas

Rectangle (Under): ∫ ≈ h·(y₀ + y₁ + ... + yₙ₋₁)

Rectangle (Over): ∫ ≈ h·(y₁ + y₂ + ... + yₙ)

Trapezoid: ∫ ≈ h·((y₀ + yₙ)/2 + y₁ + y₂ + ... + yₙ₋₁)

Simpson: ∫ ≈ h/3·(y₀ + yₙ + 4·Σ(odd) + 2·Σ(even))

Input Example

0.0 1.0
0.5 1.5
1.0 2.0
1.5 2.5
2.0 3.0

Accuracy

Simpson's method: Most accurate (4th order) Trapezoid: Good accuracy (2nd order) Rectangle: Least accurate (1st order)