Integral calculator

Integrate a polynomial and calculate a signed area between bounds.

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Polynomial in x

Lower bound

More inputs and assumptions

Upper bound

Answer

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Integrate c × x^n as c × x^(n + 1) ÷ (n + 1). The definite integral is the antiderivative at the upper bound minus its value at the lower bound.

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Formula and assumptions

Supports polynomials through degree 20, not arbitrary functions, quotients or parentheses. Reversed limits change the sign. The definite integral is signed area; it is not always total geometric area.

Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.

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Updated 2026-09-26

Using Integral calculator

Integrate c × x^n as c × x^(n + 1) ÷ (n + 1). The definite integral is the antiderivative at the upper bound minus its value at the lower bound.

Next: Derivative calculator

A worked example

With polynomial in x = 3*x^2 + 2*x + 1, lower bound = 0, upper bound = 2, the definite integral is 14.

Next: Graph functions online

Before you use the result

Example results for upper bound

These examples use Polynomial in x: 3*x^2 + 2*x + 1; Lower bound: 0. They are reference calculations, not recommended settings.

Upper bound	Definite integral
1	3
2	14
4	84

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