Integral Calculator
Definite integral shown as shaded area under the curve
About this calculator
The Integral Calculator evaluates the definite integral ∫ₐᵇ f(x) dx with a 2000-interval composite Simpson's rule and reports it three ways: the net signed integral, the total unsigned area ∫|f(x)| dx, and the average value of f over [a, b]. Bounds may be entered in either order — reversing them negates the integral, as ∫ₐᵇ = −∫ᵇₐ. Every Simpson node is checked first, so endpoint singularities like ln(0) or 1/x at 0 are reported as undefined instead of silently producing a wrong finite answer.
How to use the Integral Calculator calculator
- Enter the values for your problem into the input fields.
- Read the result — it updates instantly as you type.
- Check the formula and the visual explanation to follow how the answer was found.
- Copy the page URL to share the exact calculation.
Common examples
- ∫₀³ x² dx → 9, with average value 3 over [0, 3]
- ∫₀^π sin(x) dx → 2
- ∫₋₂² x³ dx → net integral 0 (odd symmetry) but total area 8
- ∫₁^e 1/x dx → 1, the natural-log integral
Frequently asked questions
How does the Integral Calculator calculator work?
Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.
When would I use the Integral Calculator calculator?
It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.
How accurate are the results?
Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.