Simpson's Rule Calculator
Approximate definite integrals using Simpson's numerical integration rules.
Function
Integration Bounds
Intervals (n)
Step size h = 0.250000
Evaluation Points
| x | f(x) | Coef |
|---|---|---|
| 0.0000 | 0.000000 | 1 |
| 0.2500 | 0.062500 | 4 |
| 0.5000 | 0.250000 | 2 |
| 0.7500 | 0.562500 | 4 |
| 1.0000 | 1.000000 | 1 |
Integral of x^2 from 0 to 1
0.33333333
Simpson's 1/3 Rule
Simpson's 3/8
0.33333333
Step Size (h)
0.250000
Error Analysis
Exact Value0.33333333
Absolute Error0.0000e+0
Relative Error0.000000%
Simpson's 1/3 Rule Formula
Integral = (h/3)[f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + ... + f(xn)]
Error: O(h^4) - Very accurate for smooth functions
About Simpson's Rule
- Approximates f(x) with parabolic segments
- Requires even number of intervals
- More accurate than trapezoidal rule
- Exact for polynomials up to degree 3