Simpson's Rule Calculator
Approximate definite integrals using Simpson's 1/3 rule. Enter function, limits, and number of subintervals (must be even).
Published by:
isCalculator Editorial Team
Was this calculator helpful?
How to use this tool?
How to Use the Simpson's Rule Calculator
- Enter the function f(x) in the first field. Use JavaScript syntax:
^for power,*for multiplication, and functions likeMath.sin(x). Example:x^2orMath.exp(-x^2). - Set the integration limits: enter the lower limit a and upper limit b (must be numeric, with a < b).
- Choose the number of subintervals n (must be an even number ≥ 2). Larger n gives more accuracy.
- Click "Calculate" to see the approximate integral value and step-by-step breakdown.
Output: The result is the approximate definite integral from a to b using Simpson's 1/3 rule. The steps show the function, limits, step size h, and intermediate sums.
Tip: Use an even n for the rule to work correctly. If you see an error, check your function syntax or limits.
Previous Results
| Result | Inputs | Date |
|---|
Frequently Asked Questions
Simpson's 1/3 rule is a numerical integration method that approximates the definite integral of a function using quadratic polynomials on each pair of subintervals. It requires an even number of subintervals.
Use JavaScript math syntax. For example, x^2 for x squared, Math.sin(x) for sine, Math.exp(x) for exponential. Use * for multiplication, and parentheses for grouping.
Simpson's 1/3 rule pairs two subintervals to fit a quadratic polynomial. If n is odd, the last interval cannot be paired, and the method fails.
