Definite Integral Calculator

Evaluate a definite integral over an interval.

Use this calculator as a study checker

Enter the problem carefully, review the interpreted input, and compare each step with your own work. Calculus results can depend on notation, variables, bounds, domains, and assumptions.

Check the method before copying the answer.
Use the examples below to test nearby problems.
Read the calculus guides for worked explanations.

Solution

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Enter an expression or choose an example to calculate.

Definite Integral Examples

What this calculator is for

A definite integral measures signed accumulation between a lower and upper limit. It can represent area, distance, work, probability, or total change depending on the function. Use it to check your setup, compare steps with your own work, and review the meaning of the final expression before copying it into homework.

How definite integrals are evaluated

Find an antiderivative \(F(x)\) for the integrand.
Evaluate \(F(b)-F(a)\), where \(a\) is the lower bound and \(b\) is the upper bound.
Read the sign carefully: area below the axis contributes negative signed area.

Manual example

Problem: \(\int_0^3 2x\,dx\).
An antiderivative of \(2x\) is \(x^2\).
Evaluate \([x^2]_0^3=3^2-0^2=9\).

Common mistakes to avoid

Subtracting in the wrong order.
Forgetting that signed area can be negative.
Using decimal approximations too early when an exact answer is possible.

When to double-check the result

For discontinuities or infinite bounds, use the improper integral calculator so the result is checked with limits.