Definite integral calculator
Type a function of x and the lower and upper limits, and get the definite integral: the area under the curve between those limits, counting parts below the x-axis as negative.
Use ^ for powers, * for times (optional: 3x), sqrt, sin, cos, tan, exp, log (= ln), pi and e.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
How it is calculated
The integral is calculated numerically with adaptive Simpson's rule, which keeps splitting the interval where the function changes quickly. The result is accurate to about 10 significant digits. For example, the integral of sin(x) from 0 to π is 2.
What it does not do
This tool gives the value of a definite integral, a number. It doesn't produce an antiderivative as a formula. If the function is undefined or infinite somewhere on the interval (such as 1/x at x = 0), you get a message to choose other limits.
Input
Write functions the same way as in the derivative calculator: ^ for powers, sqrt, sin, exp, log and pi. The limits may be expressions such as pi/2.
Frequently asked questions
Is the integral calculator free?
Yes. The integral calculator is completely free, with no account, sign-up or usage limit.
How accurate is the result?
The tool calculates with your browser's number precision. For important calculations, always double-check what you entered.
Does it work on my phone?
Yes. The tool works in any modern browser on a phone, tablet or computer.