How it works
Composite Simpson’s rule: h/3 × [f(a)+f(b)+4Σ odd interior samples+2Σ even interior samples], evaluating the entered polynomial with Horner’s method.
Input definitions
- Coefficients from highest power to constant
- Plain text; maximum 200,000 characters.
- Lower integration bound
- Enter the value in the labeled unit.
- Upper integration bound
- Enter the value in the labeled unit.
- Even subinterval count (2–10000)
- Enter the value in the labeled unit.
A worked example
- Coefficients from highest power to constant
- 1,0,0
- Lower integration bound
- 0
- Upper integration bound
- 3
- Even subinterval count (2–10000)
- 12
Assumptions & limits
Degree at most 20, finite bounds within ±10⁶, even interval count up to 10,000. No general expression parser or automatic error estimate.
Sources & review
Maintained by AnsRio. Methods and examples use automated checks; this does not imply independent professional certification.
Method updated 2026-10-17. Content checked against the stated method and examples. Our verification approach.
Common questions
Is a numerical integral always exact for a polynomial?
Simpson’s rule is exact for degree up to three in exact arithmetic. Higher-degree polynomials have approximation error; floating-point rounding can affect any degree. Compare results with more intervals.
How does Polynomial definite integral by Simpson’s rule work?
Composite Simpson’s rule: h/3 × [f(a)+f(b)+4Σ odd interior samples+2Σ even interior samples], evaluating the entered polynomial with Horner’s method.
What are the limits of Polynomial definite integral by Simpson’s rule?
Degree at most 20, finite bounds within ±10⁶, even interval count up to 10,000. No general expression parser or automatic error estimate.