Numerical Integration Calculator (Simpson's Rule)
Approximate a definite integral of a list of function values.
Enter your values
ⓘ Live results
Results
- Approximate integral
- 72
- Number of intervals
- 6
- Step size
- 1
Quick answer
Simpson's rule fits parabolas through pairs of intervals for a more accurate approximation than the trapezoidal rule.
∫≈(h/3)[f0+4f1+2f2+...+4f(n-1)+fn]
How to use the Numerical Integration Calculator (Simpson's Rule)
- 1List an odd number of evenly spaced function values.
- 2Enter the step size h between consecutive x values.
- 3Simpson's rule weights the values 1-4-2-4-...-4-1 and scales by h/3.
Worked example
Using the values the calculator loads with:
Inputs
- Function values (comma-separated, odd count)0,1,4,9,16,25,36
- Step size h1
Results
- Approximate integral72
- Number of intervals6
- Step size1
Frequently asked questions
Why does it need an odd count of points?
Simpson's rule pairs points into parabolic segments, requiring an even number of intervals (odd number of points).
How accurate is it?
Much more accurate than the trapezoidal rule for smooth functions, with error shrinking as h^4.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.