Calculus
Integral Calculator
Approximate definite integrals between any two bounds or evaluate an antiderivative numerically at a point.
Approximate definite integrals or evaluate an antiderivative at a point.
Integral definition
∫_a^b f(x) dx
The calculator applies adaptive Simpson’s rule behind the scenes, making it ideal for smooth functions. For indefinite results it integrates from 0 to x and reports F(x) + C.
How to use
- Enter the function f(x) using x as the variable (sin, cos, log, exp, etc. are supported).
- Choose definite mode to supply lower and upper bounds, or indefinite mode to evaluate F(x) at a point.
- Review the approximation plus any helpful context such as the evaluation point or bounds.
Example
Input: f(x) = x^2, a = 0, b = 2
Output: ∫₀² x² dx ≈ 2.6667
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Integral Calculator: integral calculator, definite integral calculator, antiderivative calculator, integral calculator step by step. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.
Deep dive & study plan
Integral Calculator: Evaluates definite integrals and approximates antiderivatives. It's built around integral, definite integral, antiderivative, so you can go from a raw question to a checked answer without switching tools.
The math behind it: The calculator applies adaptive Simpson’s rule behind the scenes, making it ideal for smooth functions. For indefinite results it integrates from 0 to x and reports F(x) + C. The core relationship is ∫_a^b f(x) dx, shown above the calculator so you can see exactly how your inputs turn into the result.
To use it well: (1) Enter the function f(x) using x as the variable (sin, cos, log, exp, etc. are supported). (2) Choose definite mode to supply lower and upper bounds, or indefinite mode to evaluate F(x) at a point. (3) Review the approximation plus any helpful context such as the evaluation point or bounds. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.
Worked example: entering f(x) = x^2, a = 0, b = 2 returns ∫₀² x² dx ≈ 2.6667. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.
FAQ & notes
Which functions are supported?
Standard JavaScript math functions (sin, cos, tan, exp, log, sqrt, etc.) are supported. Use ** for powers or write expressions like x^2 which are automatically converted.
How accurate is the result?
Simpson’s rule converges quickly for smooth functions. Increase precision by rewriting the function if it has discontinuities at the bounds.
What formula does the Integral Calculator use?
The calculator applies adaptive Simpson’s rule behind the scenes, making it ideal for smooth functions. For indefinite results it integrates from 0 to x and reports F(x) + C.
How do I use the Integral Calculator?
Enter the function f(x) using x as the variable (sin, cos, log, exp, etc. are supported). Choose definite mode to supply lower and upper bounds, or indefinite mode to evaluate F(x) at a point. Review the approximation plus any helpful context such as the evaluation point or bounds.