Maths & numbers
Adaptive numerical integration
Estimate a definite integral with an evaluation count and error estimate.
A clear answer. Here’s how.
Adaptive Simpson subdivision compares one panel with two half-panels and applies a delta/15 correction. Recursion is limited to depth 20 and 20,000 function evaluations. Reversed bounds negate the estimate; equal bounds return zero. Requires finite values and a sufficiently smooth integrand; an estimated error is not a guarantee for singular, discontinuous or highly oscillatory functions.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Expression in x
- sin(x)
- Lower X bound
- 0
- Upper X bound
- 3.141592653589793
- Absolute error target
- 1e-8
Example result
- Integral estimate
- 2
- Estimated absolute quadrature error
- 0.00000000519675166672
- Function evaluations
- 121
Adaptive Simpson estimate, assuming a sufficiently smooth finite function. The error estimate is not a proof of accuracy.