indefinite integral

Also known as: antiderivative, primitive

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June 29, 2026

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An indefinite integral, also known as an antiderivative, is a function whose derivative is a given function. This concept is a fundamental part of calculus, a branch of mathematics concerned with rates of change and accumulation.123

The indefinite integral is represented by the integral sign \u222b followed by the function and dx, which signifies an infinitesimal displacement along the x-axis. For example, \u222bf(x)dx represents the summation of the product of f(x) and dx.3

Because the derivative of a constant is zero, an indefinite integral is not unique; it includes an arbitrary constant, often denoted as C. The process of finding an indefinite integral is called integration. Integration techniques are used to solve problems involving area, volume, and other quantities that can be interpreted as the area under a curve.13

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calculus
Differentiation and integration
This is called the (indefinite) integral of the function y = x², and it is written as ∫x²dx. The initial symbol ∫ is an elongated S, which stands for sum, and dx indicates an infinitely small increment of the variable, or axis, over which the function is being summed.…
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This is called the (indefinite) integral of the function y = x², and it is written as ∫x²dx. The initial symbol ∫ is an elongated S, which stands for sum, and dx indicates an infinitely small increment of the variable, or axis, over which the function is being summed.…
Read More

integral
An indefinite integral, sometimes called an antiderivative, of a function f(x), denoted byis a function the derivative of which is f(x). Because the derivative of a constant is zero, the indefinite integral is not unique. The process of finding an indefinite integral is called integration.
Read More
An indefinite integral, sometimes called an antiderivative, of a function f(x), denoted byis a function the derivative of which is f(x). Because the derivative of a constant is zero, the indefinite integral is not unique. The process of finding an indefinite integral is called integration.
Read More