How to use it
- Type the function of x, for example 3x^2 + 2x - 1 or sin(x).
- Enter the lower limit a and the upper limit b.
- For polynomials you get the antiderivative F(x) + C and the exact value F(b) − F(a). For other functions you get an accurate numeric value.
What a definite integral means
The definite integral from a to b measures the signed area between the curve and the x-axis. Area above the axis counts as positive, and area below counts as negative.
The fundamental theorem of calculus
If F is an antiderivative of f, then the integral from a to b equals F(b) − F(a). For f(x) = 3x² + 2x − 1, F(x) = x³ + x² − x, so the integral from 0 to 2 is (8 + 4 − 2) − 0 = 10.
How non-polynomial functions are handled
For functions such as sin(x), eˣ or 1/x, the calculator uses Simpson's rule with 2,000 intervals. It is accurate to many decimal places for smooth functions. If the function is undefined inside the interval, the calculator tells you.
Frequently asked questions
Why do only polynomials get an antiderivative?
The exact antiderivative is computed with the power rule, which covers polynomials. Other functions get a precise numeric value for the definite integral.
Can the result be negative?
Yes. The definite integral is a signed area, so parts below the x-axis count as negative.
Does it use degrees or radians?
Radians, as calculus formulas require.
What if a is larger than b?
The result changes sign: the integral from b to a is the negative of the integral from a to b.