Regra de Simpson 1/3 (1 passo)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
Simpson 1/3
About this calculator
The Simpson's 1/3 Rule calculator (single step) numerically computes the definite integral of a function f(x) between two limits a and b. It uses the formula (h/3)*(f(a) + 4*f(m) + f(b)), where h = (b-a)/2 and m = (a+b)/2 is the midpoint. This technique approximates the area under the curve by fitting a parabola through the three points (a, f(a)), (m, f(m)), and (b, f(b)).
This method is useful when the analytical integral is difficult or impossible to compute, such as for complex functions or experimental data. For example, in engineering to calculate work done by a varying force, or in physics to determine displacement from velocity data. Simpson's rule provides good accuracy for smooth functions with continuous derivatives.
Important precautions: Simpson's 1/3 rule with a single step (two subintervals) may not be accurate for functions with sharp variations or over large intervals. In such cases, consider using the composite Simpson's rule (multiple steps) or other numerical integration methods. Additionally, the function must be continuous on the interval [a,b] to avoid errors.
Frequently asked questions
How does Simpson's 1/3 Rule compute the integral?
It divides the interval into two equal subintervals, fits a parabola through the three points (a, f(a)), (m, f(m)), and (b, f(b)), and calculates the area under the parabola using the formula (h/3)*(f(a)+4f(m)+f(b)).
What is the difference between simple and composite Simpson's 1/3?
The simple version uses only one step (two subintervals), while the composite divides the interval into more even subintervals, applying the rule repeatedly for higher accuracy.
Does this calculator work for non-polynomial functions?
Yes, it works for any continuous function, but accuracy depends on the function's smoothness. For highly oscillatory functions, the composite rule is recommended.
Do I need to input the function in a special way?
Yes, enter the function using JavaScript syntax, such as Math.sin(x) for sine, Math.exp(x) for exponential, and standard operators (+, -, *, /, ^ for power).
What does '1 step' mean in Simpson's 1/3 Rule?
It means the interval [a,b] is divided into only two subintervals (n=2), using the three points: a, the midpoint, and b. This is the simplest form of the method.