Definite Integral Calculator
Numerically evaluate ∫ f(x) dx over [a, b] using composite Simpson’s rule.
How it works
- 1Enter any expression in x — e.g. x^2, sin(x), or exp(-x^2) — in the function field.
- 2Set the lower limit a and upper limit b; the tool evaluates ∫ f(x) dx from a to b using composite Simpson’s rule with 1,000 subintervals.
- 3The result updates instantly. If a > b the calculator returns the negative of the integral, matching the signed-area definition.
Use cases
- Physics: computing displacement from a velocity function over a time interval.
- Engineering: finding the area under a load curve or signal envelope without hand integration.
- Maths: checking an analytic antiderivative against a numerical benchmark.
Frequently asked questions
How accurate is the result?
Composite Simpson’s rule with 1,000 subintervals gives errors of order h⁴, well within double-precision floating point for smooth functions. Accuracy drops near discontinuities or rapid oscillations.
Which functions can I use?
Operators +, −, ×, ÷, ^, parentheses, and functions sin, cos, tan, asin, acos, atan, sqrt, cbrt, abs, exp, ln, log. Constants pi and e are recognised; the only variable is x.
What happens when a equals b?
When a = b the integral is exactly 0 — integrating over an interval of zero width encloses no area.
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