Online Tool Store
Integral Calculator
Type a function of x and a lower and upper bound to get a numerically estimated definite integral, computed instantly with Simpson's rule.
🔒 This tool runs entirely in your browser. Your files are never uploaded to a server.
Definite integral
How the integral calculator works
- Type a function of x — arithmetic, common functions like sin and sqrt, and the constants pi and e are all supported.
- Enter a lower bound (a) and upper bound (b) for the definite integral.
- The calculator numerically estimates the area under the curve between a and b, updating instantly as you type.
The method
A definite integral is the signed area between a curve and the x-axis over an interval. This calculator estimates it with composite Simpson's rule, which fits a parabola through each pair of adjacent subintervals rather than a straight line (as the simpler trapezoidal rule does) — that extra curvature makes it far more accurate for smooth functions with the same number of subintervals:
∫ₐᵇ f(x) dx ≈ (h/3) × [f(a) + 4f(x₁) + 2f(x₂) + 4f(x₃) + … + f(b)]
Example: ∫₀^π x² sin(x) dx evaluates to about π² − 4 ≈ 5.87, which this calculator's default example reproduces numerically.
FAQ
Does this give an exact symbolic answer?
No — this calculator estimates the definite integral numerically (using Simpson's rule), not symbolically. It won't return an answer in terms of a formula, but the numeric result is accurate to a small fraction of a percent for smooth, well-behaved functions.
What functions and operators are supported?
Standard arithmetic (+ − × ÷ ^), parentheses, sin, cos, tan, sqrt, exp, ln, log (base 10), abs, and the constants pi and e. Use x as your variable, e.g. x^2 * sin(x).
What happens if my function is undefined somewhere in the interval?
The calculator flags an error rather than showing a misleading number — a function like 1/x integrated across x = 0, for example, isn't something Simpson's rule can evaluate reliably.
Is my function or the result sent anywhere?
No. The expression is parsed and evaluated by a small parser running entirely in your browser — nothing is sent to Online Tool Store or any other server.
How we compare
| Feature | Online Tool Store | Symbolab | WolframAlpha |
|---|---|---|---|
| Instant result as you type | ✓ | Calculate button | Calculate button |
| No sign-up or daily query limit | ✓ | Limited free queries | Limited free queries |
| Runs entirely on your device | ✓ | Server-side computation | Server-side computation |
For a quick numeric estimate of a definite integral without hitting a query limit, the Online Tool Store Integral Calculator computes it instantly on your own device.