About This Calculator
This Simpson's Rule error bound calculator estimates the maximum possible error when approximating a definite integral using Simpson’s Rule. It is useful in numerical analysis and applied mathematics to evaluate integration accuracy.
How It Works
The error bound formula for Simpson’s Rule is:
Enter the integration limits (a and b) and the maximum value of the 4th derivative over [a, b]. The calculator then computes the upper bound of the integration error.
Frequently Asked Questions
What is Simpson’s Rule?
Simpson’s Rule is a numerical method for approximating definite integrals using quadratic polynomials.
What does the error bound mean?
The error bound estimates the maximum possible deviation between the numerical approximation and the exact integral.
Why is the 4th derivative used?
The 4th derivative determines the accuracy of the quadratic approximation in Simpson’s Rule and directly influences the error bound.
Can this be used for all functions?
Simpson’s Rule applies to functions that are sufficiently smooth and differentiable up to the 4th order on the interval [a, b].
Is Simpson’s Rule more accurate than Trapezoidal Rule?
Yes, Simpson’s Rule usually provides higher accuracy because it uses quadratic instead of linear approximations.