Integral Calculator
Integral Calculator works out Antiderivative and Integral from What to compute, Integrand f(x) and Integrate with respect to. The default figures on this page give antiderivative of x^3 / 3 + C; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
3 steps
- Integrand: f(x) = x^2
- Antiderivative: F(x) = x^3 / 3
- Check by differentiating back: d/dx [F(x)] = x^2, which is the integrand.
Its 6 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
3 sources
What the Integral Calculator calculates
Finds the indefinite integral (antiderivative) of an expression symbolically and evaluates definite integrals, verifying every symbolic answer by differentiating it back and cross-checking definite values against numeric quadrature.
How to use this Integral Calculator
Enter What to compute, Integrand f(x), Integrate with respect to and Lower limit a. Antiderivative updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Antiderivative, Integral and Value of the definite integral.
The method follows OpenStax, Calculus Volume 1, chapter 5: Integration (the definite integral, the Fundamental Theorem of Calculus, substitution), OpenStax, Calculus Volume 2, section 3.1: Integration by Parts and NIST Digital Library of Mathematical Functions, chapter 4: Elementary Functions (antiderivative table).
Power rule: the antiderivative of x^2 example
With What to compute: indefinite, Integrand f(x): x^2, Integrate with respect to: x, the calculator returns Antiderivative: x^3 / 3 + C, Verified by differentiating back: yes. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Antiderivative, Integral and Value of the definite integral. The inputs you can vary are What to compute, Integrand f(x), Integrate with respect to, Lower limit a, Upper limit b and Decimal places in the numeric answer.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How to do an integral on a calculator?
Finds the indefinite integral (antiderivative) of an expression symbolically and evaluates definite integrals, verifying every symbolic answer by differentiating it back and cross-checking definite values against. Open “How this is worked out” beside the result to see each step for your own figures.
Are integrals in Calc 1 or 2?
Finds the indefinite integral (antiderivative) of an expression symbolically and evaluates definite integrals, verifying every symbolic answer by differentiating it back and cross-checking definite values against. Put your own figures in above and the working updates beside the result. For scale, the default figures on this page give x^3 / 3 + C.
Can a TI-84 calculator do integrals?
It needs What to compute, Integrand f(x), Integrate with respect to, Lower limit a, Upper limit b and Decimal places in the numeric answer. Nothing else is required, and the figures stay in your browser.
Can a TI-84 do indefinite integrals?
The result gives Antiderivative, Integral, Value of the definite integral, How it was evaluated, Verified by differentiating back and F(a), each labelled with its unit so the figure can be read on its own.
What information do I need for the Integral Calculator?
You need What to compute, Integrand f(x), Integrate with respect to, Lower limit a, Upper limit b and Decimal places in the numeric answer. The page opens with default figures that give antiderivative of x^3 / 3 + C, so you can see the scale before entering your own.
What does this Integral Calculator show?
It shows Antiderivative, Integral, Value of the definite integral, How it was evaluated, Verified by differentiating back, F(a), F(b) and Value rounded for display, with the working and any warnings for your entries.