NIntegrate

NIntegrate(f, {x,a,b})

computes the numerical univariate real integral of f with respect to x from a to b.

See:

• Wikipedia - Numerical integration
• Wikipedia - Trapezoidal rule
• Wikipedia - Romberg’s method
• Wikipedia - Riemann sum
• Wikipedia - Truncation error (numerical integration)
• Wikipedia - Gauss-Kronrod quadrature formula)

Examples

>> NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1})
-0.0208333333333333

LegendreGauss is the default method for numerical integration

>> NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1}, Method->LegendreGauss)
-0.0208333333333333

>> NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1}, Method->Simpson)
-0.0208333320915699

>> NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1}, Method->Trapezoid)
-0.0208333271245165

>> NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1}, Method->Romberg)
-0.0208333333333333

>> NIntegrate(Exp(-x^2),{x,-Infinity,Infinity}, Method->GaussKronrod)
1.772453850905516

>> NIntegrate(Cos(200*x),{x,0,1}, Method->GaussKronrod)
-0.004366486486070

Other options include MaxIterations and MaxPoints

>> NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1}, Method->Trapezoid, MaxIterations->5000)
-0.0208333271245165

Related terms

D, DSolve, Integrate, Limit, ND

Implementation status

• ☑ - partially implemented

Github

• Implementation of NIntegrate