Integrals

∫ Integrals

$\int_a^b f(x)\,dx$

Trapezoidal Rule

Func<double, double> f = x => Math.Sin(x);
double integral = f.Integrate(0, Math.PI);

Simpson's 1/3 Rule — O(h⁴) accuracy

double result = f.IntegrateSimpson(0, Math.PI, subintervals: 200);

Simpson's 3/8 Rule — cubic interpolation, O(h⁴)

double result = f.IntegrateSimpson38(0, Math.PI, subintervals: 999);

Gauss-Legendre Quadrature — 5-point per subinterval, very high accuracy

double result = f.IntegrateGaussLegendre(0, Math.PI, subintervals: 10);

Romberg Integration — Richardson extrapolation for rapid convergence

double result = f.IntegrateRomberg(0, Math.PI, maxLevel: 10);

Adaptive Simpson — recursive subdivision with error control

double result = f.IntegrateAdaptive(0, Math.PI, tolerance: 1e-12);

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🎲 Monte Carlo Integration

$\iint_D f(x,y)\,dA, \quad \iiint_V f(x,y,z)\,dV$

Double integral

Func<(double x, double y), double> func2d = p => p.x * p.y;
double result2d = func2d.Integrate((0, 1), (0, 1));

Triple integral

Func<Vector, double> func3d = v => v.x + v.y + v.z;
double result3d = func3d.Integrate(new Vector(-2, -2, -2), new Vector(2, 2, 2));

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📈 Series / Time Series Integration

List<TimeSerie> ts = ...;
double total = ts.Integrate();
double bounded = ts.Integrate(startDate, endDate);