About the Numerical Integration Calculator
Compare trapezoidal rule, Simpson's rule and Gauss–Legendre quadrature for any integral, with each method's error.
Also known as: simpson's rule calculator, trapezoid rule calculator, gaussian quadrature, numerical integral.
How to use this calculator
- Enter f(x), a, b, intervals n.
- The result updates instantly as you type — press Calculate (or Enter) at any time.
- Review the breakdown shown under the main result.
- Use Copy result or Share to save the answer or send a link with your inputs.
Formula
Trapezoid: h/2·[f₀ + 2f₁ + … + fₙ] · Simpson: h/3·[f₀ + 4f₁ + 2f₂ + … + fₙ]
Worked example
Using the values pre-filled in the calculator above:
- f(x): sqrt(1 + x^3)
- a = 0
- b = 2
- Intervals n = 10
the calculator returns:
- Best estimate (adaptive): 3.241309263195